{ "cells": [ { "cell_type": "markdown", "id": "6c1dc4d7", "metadata": { "originalKey": "e23719d9-8a24-4208-8439-34e7b8270c79", "papermill": { "duration": 0.003422, "end_time": "2024-05-02T05:16:30.491917", "exception": false, "start_time": "2024-05-02T05:16:30.488495", "status": "completed" }, "tags": [] }, "source": [ "# Visualizations\n", "\n", "This tutorial illustrates the core visualization utilities available in Ax." ] }, { "cell_type": "code", "execution_count": 1, "id": "8f82cb6a", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-05-02T05:16:30.499785Z", "iopub.status.busy": "2024-05-02T05:16:30.499338Z", "iopub.status.idle": "2024-05-02T05:16:33.963647Z", "shell.execute_reply": "2024-05-02T05:16:33.962874Z" }, "executionStartTime": 1627652821316, "executionStopTime": 1627652822868, "hidden_ranges": [], "originalKey": "101b0e96-5b3d-48c5-bf3c-677b4ddf90c7", "papermill": { "duration": 3.482263, "end_time": "2024-05-02T05:16:33.977358", "exception": false, "start_time": "2024-05-02T05:16:30.495095", "status": "completed" }, "requestMsgId": "c0dd9aaf-896d-4ea9-912f-1e58d301d114", "tags": [] }, "outputs": [ { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:33] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:33] ax.utils.notebook.plotting: Please see\n", " (https://ax.dev/tutorials/visualizations.html#Fix-for-plots-that-are-not-rendering)\n", " if visualizations are not rendering.\n" ] }, { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "from ax.modelbridge.cross_validation import cross_validate\n", "from ax.plot.contour import interact_contour\n", "from ax.plot.diagnostic import interact_cross_validation\n", "from ax.plot.scatter import interact_fitted, plot_objective_vs_constraints, tile_fitted\n", "from ax.plot.slice import plot_slice\n", "from ax.service.ax_client import AxClient, ObjectiveProperties\n", "from ax.utils.measurement.synthetic_functions import hartmann6\n", "from ax.utils.notebook.plotting import init_notebook_plotting, render\n", "\n", "init_notebook_plotting()" ] }, { "cell_type": "markdown", "id": "d9852c74", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "8449378f-890e-4e76-8d73-ce2aa4120a69", "papermill": { "duration": 0.032077, "end_time": "2024-05-02T05:16:34.041888", "exception": false, "start_time": "2024-05-02T05:16:34.009811", "status": "completed" }, "showInput": true, "tags": [] }, "source": [ "## 1. Create experiment and run optimization\n", "\n", "The vizualizations require an experiment object and a model fit on the evaluated data. The routine below is a copy of the Service API tutorial, so the explanation here is omitted. Retrieving the experiment and model objects for each API paradigm is shown in the respective tutorials" ] }, { "cell_type": "markdown", "id": "2d5f015f", "metadata": { "originalKey": "f7544e06-6c6a-4841-b659-3be6a198a948", "papermill": { "duration": 0.031777, "end_time": "2024-05-02T05:16:34.105501", "exception": false, "start_time": "2024-05-02T05:16:34.073724", "status": "completed" }, "tags": [] }, "source": [ "#### 1a. Define search space and evaluation function" ] }, { "cell_type": "code", "execution_count": 2, "id": "4e69cd61", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-05-02T05:16:34.171162Z", "iopub.status.busy": "2024-05-02T05:16:34.170574Z", "iopub.status.idle": "2024-05-02T05:16:34.175520Z", "shell.execute_reply": "2024-05-02T05:16:34.174936Z" }, "executionStartTime": 1627652824829, "executionStopTime": 1627652824877, "hidden_ranges": [], "originalKey": "28f6cb76-828f-445d-bdda-ba057c87dcd0", "papermill": { "duration": 0.039321, "end_time": "2024-05-02T05:16:34.176855", "exception": false, "start_time": "2024-05-02T05:16:34.137534", "status": "completed" }, "requestMsgId": "7495e7e2-1025-4292-b3aa-e953739cef3e", "tags": [] }, "outputs": [], "source": [ "noise_sd = 0.1\n", "param_names = [f\"x{i+1}\" for i in range(6)] # x1, x2, ..., x6\n", "\n", "\n", "def noisy_hartmann_evaluation_function(parameterization):\n", " x = np.array([parameterization.get(p_name) for p_name in param_names])\n", " noise1, noise2 = np.random.normal(0, noise_sd, 2)\n", "\n", " return {\n", " \"hartmann6\": (hartmann6(x) + noise1, noise_sd),\n", " \"l2norm\": (np.sqrt((x**2).sum()) + noise2, noise_sd),\n", " }" ] }, { "cell_type": "markdown", "id": "50caa7a2", "metadata": { "originalKey": "17a51543-298e-47d4-bcd9-33459fe1169e", "papermill": { "duration": 0.032071, "end_time": "2024-05-02T05:16:34.241004", "exception": false, "start_time": "2024-05-02T05:16:34.208933", "status": "completed" }, "tags": [] }, "source": [ "#### 1b. Create Experiment" ] }, { "cell_type": "code", "execution_count": 3, "id": "ecf7311a", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-05-02T05:16:34.307050Z", "iopub.status.busy": "2024-05-02T05:16:34.306449Z", "iopub.status.idle": "2024-05-02T05:16:34.321647Z", "shell.execute_reply": "2024-05-02T05:16:34.321121Z" }, "executionStartTime": 1627654956712, "executionStopTime": 1627654956823, "hidden_ranges": [], "originalKey": "6fca889c-a4ff-42ef-a669-6eb8803de89c", "papermill": { "duration": 0.049812, "end_time": "2024-05-02T05:16:34.322894", "exception": false, "start_time": "2024-05-02T05:16:34.273082", "status": "completed" }, "requestMsgId": "905eff52-e649-4bd5-abf0-ff69c1549852", "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Starting optimization with verbose logging. To disable logging, set the `verbose_logging` argument to `False`. Note that float values in the logs are rounded to 6 decimal points.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.utils.instantiation: Created search space: SearchSpace(parameters=[RangeParameter(name='x1', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x2', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x3', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x4', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x5', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x6', parameter_type=FLOAT, range=[0.0, 1.0])], parameter_constraints=[]).\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: Using Models.BOTORCH_MODULAR since there is at least one ordered parameter and there are no unordered categorical parameters.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: Calculating the number of remaining initialization trials based on num_initialization_trials=None max_initialization_trials=None num_tunable_parameters=6 num_trials=None use_batch_trials=False\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=12\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=12\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: `verbose`, `disable_progbar`, and `jit_compile` are not yet supported when using `choose_generation_strategy` with ModularBoTorchModel, dropping these arguments.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+BoTorch', steps=[Sobol for 12 trials, BoTorch for subsequent trials]). Iterations after 12 will take longer to generate due to model-fitting.\n" ] } ], "source": [ "ax_client = AxClient()\n", "ax_client.create_experiment(\n", " name=\"test_visualizations\",\n", " parameters=[\n", " {\n", " \"name\": p_name,\n", " \"type\": \"range\",\n", " \"bounds\": [0.0, 1.0],\n", " }\n", " for p_name in param_names\n", " ],\n", " objectives={\"hartmann6\": ObjectiveProperties(minimize=True)},\n", " outcome_constraints=[\"l2norm <= 1.25\"],\n", ")" ] }, { "cell_type": "markdown", "id": "15ca0871", "metadata": { "code_folding": [], "hidden_ranges": [], "originalKey": "ab892f7c-4830-4c1d-b476-ec1078ec3faf", "papermill": { "duration": 0.032802, "end_time": "2024-05-02T05:16:34.388617", "exception": false, "start_time": "2024-05-02T05:16:34.355815", "status": "completed" }, "showInput": false, "tags": [] }, "source": [ "#### 1c. Run the optimization and fit a GP on all data" ] }, { "cell_type": "code", "execution_count": 4, "id": "7a6d9287", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-05-02T05:16:34.455898Z", "iopub.status.busy": "2024-05-02T05:16:34.455389Z", "iopub.status.idle": "2024-05-02T05:17:36.228125Z", "shell.execute_reply": "2024-05-02T05:17:36.227379Z" }, "executionStartTime": 1627654642967, "executionStopTime": 1627654862819, "hidden_ranges": [], "originalKey": "7269a5ba-45c8-4acf-ac83-a5ea8a52d6c1", "papermill": { "duration": 61.808527, "end_time": "2024-05-02T05:17:36.230036", "exception": false, "start_time": "2024-05-02T05:16:34.421509", "status": "completed" }, "requestMsgId": "c7a4dea8-fd6d-4e1a-84de-ad973ede0cd7", "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.020896, 'x2': 0.904968, 'x3': 0.000168, 'x4': 0.49008, 'x5': 0.194316, 'x6': 0.651144} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.130186, 0.1), 'l2norm': (1.251495, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.254904, 'x2': 0.276718, 'x3': 0.568393, 'x4': 0.137626, 'x5': 0.391328, 'x6': 0.024703} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.056309, 0.1), 'l2norm': (0.892053, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.351547, 'x2': 0.844315, 'x3': 0.191608, 'x4': 0.697669, 'x5': 0.313083, 'x6': 0.296609} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-1.19481, 0.1), 'l2norm': (1.296905, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.832836, 'x2': 0.349403, 'x3': 0.238205, 'x4': 0.109476, 'x5': 0.005529, 'x6': 0.822927} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.193561, 0.1), 'l2norm': (1.256255, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.563354, 'x2': 0.082045, 'x3': 0.68168, 'x4': 0.419048, 'x5': 0.321608, 'x6': 0.149029} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.209781, 0.1), 'l2norm': (1.2362, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.991218, 'x2': 0.712046, 'x3': 0.752436, 'x4': 0.873299, 'x5': 0.324084, 'x6': 0.921131} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.181936, 0.1), 'l2norm': (1.971424, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.380349, 'x2': 0.962953, 'x3': 0.238626, 'x4': 0.032358, 'x5': 0.284958, 'x6': 0.949175} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.177029, 0.1), 'l2norm': (1.613896, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.208664, 'x2': 0.846691, 'x3': 0.267054, 'x4': 0.969681, 'x5': 0.688151, 'x6': 0.634725} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (0.090669, 0.1), 'l2norm': (1.578328, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.946795, 'x2': 0.012834, 'x3': 0.325507, 'x4': 0.724636, 'x5': 0.891541, 'x6': 0.861132} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (0.065115, 0.1), 'l2norm': (1.706824, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.285428, 'x2': 0.250466, 'x3': 0.780617, 'x4': 0.386558, 'x5': 0.664229, 'x6': 0.263374} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.199322, 0.1), 'l2norm': (1.218192, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.989678, 'x2': 0.572212, 'x3': 0.975391, 'x4': 0.558608, 'x5': 0.022497, 'x6': 0.521227} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (0.06357, 0.1), 'l2norm': (1.755731, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.651035, 'x2': 0.364688, 'x3': 0.082868, 'x4': 0.353762, 'x5': 0.399629, 'x6': 0.966862} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:34] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.666637, 0.1), 'l2norm': (1.334875, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:40] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.279645, 'x2': 0.749335, 'x3': 0.154641, 'x4': 0.581262, 'x5': 0.27916, 'x6': 0.295518} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:40] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-0.862992, 0.1), 'l2norm': (0.967496, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:50] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.328462, 'x2': 0.794214, 'x3': 0.17621, 'x4': 0.63412, 'x5': 0.302644, 'x6': 0.281129} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:50] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-1.236234, 0.1), 'l2norm': (1.124293, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:59] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.392765, 'x2': 0.797215, 'x3': 0.18389, 'x4': 0.634274, 'x5': 0.312027, 'x6': 0.232323} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:16:59] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-1.536154, 0.1), 'l2norm': (1.122452, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:17:03] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.443493, 'x2': 0.783815, 'x3': 0.162403, 'x4': 0.595586, 'x5': 0.292667, 'x6': 0.222745} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:17:03] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-1.686711, 0.1), 'l2norm': (1.276556, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:17:13] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.432242, 'x2': 0.736396, 'x3': 0.198184, 'x4': 0.579148, 'x5': 0.317132, 'x6': 0.169138} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:17:13] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-1.983579, 0.1), 'l2norm': (1.02437, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:17:21] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.461549, 'x2': 0.722245, 'x3': 0.222253, 'x4': 0.587152, 'x5': 0.335408, 'x6': 0.102965} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:17:21] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-2.348686, 0.1), 'l2norm': (1.208449, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:17:28] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.489926, 'x2': 0.721081, 'x3': 0.226895, 'x4': 0.53872, 'x5': 0.345407, 'x6': 0.049004} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:17:28] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.427052, 0.1), 'l2norm': (1.106857, 0.1)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:17:36] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.522741, 'x2': 0.671707, 'x3': 0.232624, 'x4': 0.62002, 'x5': 0.341954, 'x6': 0.030279} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:17:36] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-1.548812, 0.1), 'l2norm': (1.058702, 0.1)}.\n" ] } ], "source": [ "for i in range(20):\n", " parameters, trial_index = ax_client.get_next_trial()\n", " # Local evaluation here can be replaced with deployment to external system.\n", " ax_client.complete_trial(\n", " trial_index=trial_index, raw_data=noisy_hartmann_evaluation_function(parameters)\n", " )" ] }, { "cell_type": "markdown", "id": "d7f351da", "metadata": { "originalKey": "72f4d3e7-fa04-43d0-8451-ded292e705df", "papermill": { "duration": 0.047521, "end_time": "2024-05-02T05:17:36.332947", "exception": false, "start_time": "2024-05-02T05:17:36.285426", "status": "completed" }, "tags": [] }, "source": [ "## 2. Contour plots\n", "\n", "The plot below shows the response surface for `hartmann6` metric as a function of the `x1`, `x2` parameters.\n", "\n", "The other parameters are fixed in the middle of their respective ranges, which in this example is 0.5 for all of them." ] }, { "cell_type": "code", "execution_count": 5, "id": "2deffc91", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-05-02T05:17:36.405698Z", "iopub.status.busy": "2024-05-02T05:17:36.405098Z", "iopub.status.idle": "2024-05-02T05:17:37.324237Z", "shell.execute_reply": "2024-05-02T05:17:37.323410Z" }, "executionStartTime": 1627654870209, "executionStopTime": 1627654871972, "hidden_ranges": [], "originalKey": "843df85c-965d-4a83-9fe1-696225d81c0f", "papermill": { "duration": 0.959901, "end_time": "2024-05-02T05:17:37.328905", "exception": false, "start_time": "2024-05-02T05:17:36.369004", "status": "completed" }, "requestMsgId": "4a643541-867c-46b6-868d-64337920c2a3", "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:17:36] ax.service.ax_client: Retrieving contour plot with parameter 'x1' on X-axis and 'x2' on Y-axis, for metric 'hartmann6'. Remaining parameters are affixed to the middle of their range.\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "autocolorscale": false, "autocontour": true, "colorbar": { "tickfont": { "size": 8 }, "ticksuffix": "", "x": 0.45, "y": 0.5 }, "colorscale": [ [ 0.0, "rgb(247,252,253)" ], [ 0.125, "rgb(229,245,249)" ], [ 0.25, "rgb(204,236,230)" ], [ 0.375, "rgb(153,216,201)" ], [ 0.5, "rgb(102,194,164)" ], [ 0.625, "rgb(65,174,118)" ], [ 0.75, "rgb(35,139,69)" ], [ 0.875, "rgb(0,109,44)" ], [ 1.0, "rgb(0,68,27)" ] ], "contours": { "coloring": "heatmap" }, "hoverinfo": "x+y+z", "ncontours": 25, "type": "contour", "x": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 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], "tickfont": { "size": 11 }, "tickmode": "auto", "title": { "text": "x2" }, "type": "linear" }, "yaxis2": { "anchor": "x2", "autorange": false, "domain": [ 0, 1 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# this could alternately be done with `ax.plot.contour.plot_contour`\n", "render(ax_client.get_contour_plot(param_x=\"x1\", param_y=\"x2\", metric_name=\"hartmann6\"))" ] }, { "cell_type": "markdown", "id": "3d710630", "metadata": { "originalKey": "1de0991a-d99b-4d07-acec-4a2eb4a20a73", "papermill": { "duration": 0.049743, "end_time": "2024-05-02T05:17:37.428540", "exception": false, "start_time": "2024-05-02T05:17:37.378797", "status": "completed" }, "tags": [] }, "source": [ "#### 2a. Interactive contour plot\n", "\n", "The plot below allows toggling between different pairs of parameters to view the contours." ] }, { "cell_type": "code", "execution_count": 6, "id": "bcda356b", "metadata": { "code_folding": [], "execution": { "iopub.execute_input": "2024-05-02T05:17:37.529412Z", "iopub.status.busy": "2024-05-02T05:17:37.528802Z", "iopub.status.idle": "2024-05-02T05:17:57.840701Z", "shell.execute_reply": "2024-05-02T05:17:57.839681Z" }, "executionStartTime": 1627652959076, "executionStopTime": 1627652982911, "hidden_ranges": [], "originalKey": "4af9f166-0163-4ff5-9ecb-f534a69efe3d", "papermill": { "duration": 20.489529, "end_time": "2024-05-02T05:17:57.967688", "exception": false, "start_time": "2024-05-02T05:17:37.478159", "status": "completed" }, "requestMsgId": "2de6919e-92e1-4425-8d90-b117e9f41855", "tags": [] }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", 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"linear" } ], "label": "x3", "method": "update" }, { "args": [ { "visible": [ false, false, false, false, false, false, false, false, false, false, false, false, true, true, true, true, false, false, false, false, false, false, false, false ] }, { "yaxis.range": [ 0.0, 1.0 ], "yaxis.title": "x4", "yaxis.type": "linear", "yaxis2.range": [ 0.0, 1.0 ], "yaxis2.type": "linear" } ], "label": "x4", "method": "update" }, { "args": [ { "visible": [ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, true, true, true, true, false, false, false, false ] }, { "yaxis.range": [ 0.0, 1.0 ], "yaxis.title": "x5", "yaxis.type": "linear", "yaxis2.range": [ 0.0, 1.0 ], "yaxis2.type": "linear" } ], "label": "x5", "method": "update" }, { "args": [ { "visible": [ false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, false, true, true, true, true ] }, { "yaxis.range": [ 0.0, 1.0 ], "yaxis.title": "x6", "yaxis.type": "linear", "yaxis2.range": [ 0.0, 1.0 ], "yaxis2.type": "linear" } ], "label": "x6", "method": "update" } ], "direction": "up", "x": 0.35, "xanchor": "left", "y": -0.43, "yanchor": "middle" } ], "width": 950, "xaxis": { "anchor": "y", "autorange": false, "domain": [ 0.05, 0.45 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "title": { "text": "x1" }, "type": "linear" }, "xaxis2": { "anchor": "y2", "autorange": false, "domain": [ 0.6, 1 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "title": { "text": "x1" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": false, "domain": [ 0, 1 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "title": { "text": "x2" }, "type": "linear" }, "yaxis2": { "anchor": "x2", "autorange": false, "domain": [ 0, 1 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model = ax_client.generation_strategy.model\n", "render(interact_contour(model=model, metric_name=\"hartmann6\"))" ] }, { "cell_type": "markdown", "id": "d1d1486b", "metadata": { "originalKey": "1ff470bb-5daf-4179-b814-01cc80dafe3e", "papermill": { "duration": 0.514934, "end_time": "2024-05-02T05:17:58.996278", "exception": false, "start_time": "2024-05-02T05:17:58.481344", "status": "completed" }, "tags": [] }, "source": [ "## 3. Tradeoff plots\n", "This plot illustrates the tradeoffs achievable for 2 different metrics. The plot takes the x-axis metric as input (usually the objective) and allows toggling among all other metrics for the y-axis.\n", "\n", "This is useful to get a sense of the pareto frontier (i.e. what is the best objective value achievable for different bounds on the constraint)" ] }, { "cell_type": "code", "execution_count": 7, "id": "2fe1f3bd", "metadata": { "execution": { "iopub.execute_input": "2024-05-02T05:18:00.021483Z", "iopub.status.busy": "2024-05-02T05:18:00.020845Z", "iopub.status.idle": "2024-05-02T05:18:00.141071Z", "shell.execute_reply": "2024-05-02T05:18:00.140379Z" }, "executionStartTime": 1627652996903, "executionStopTime": 1627652997294, "originalKey": "57023556-0293-44ef-91d6-81b911ff41d3", "papermill": { "duration": 0.634572, "end_time": "2024-05-02T05:18:00.142688", "exception": false, "start_time": "2024-05-02T05:17:59.508116", "status": "completed" }, "requestMsgId": "10b72ecc-a019-42a1-8358-18f14927ef75", "tags": [] }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "error_x": { "array": [ 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196 ], "color": "rgba(128,177,211,0.4)", "type": "data" }, "error_y": { "array": [ 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196 ], "color": "rgba(128,177,211,0.4)", "type": "data" }, "hoverinfo": "text", "marker": { "color": "rgba(128,177,211,1)" }, "mode": "markers", "name": "In-sample", "showlegend": true, "text": [ "Arm 0_0

hartmann6: -0.13 [-0.326, 0.066]
l2norm: 1.251 [1.055, 1.447]

Parameterization:
x1: 0.02089630253612995
x2: 0.9049676060676575
x3: 0.00016842130571603775
x4: 0.49008020758628845
x5: 0.1943160742521286
x6: 0.6511437296867371", "Arm 1_0

hartmann6: -0.056 [-0.252, 0.140]
l2norm: 0.892 [0.696, 1.088]

Parameterization:
x1: 0.2549036853015423
x2: 0.2767183566465974
x3: 0.5683933552354574
x4: 0.1376255163922906
x5: 0.39132768474519253
x6: 0.024703498929739", "Arm 2_0

hartmann6: -1.195 [-1.391, -0.999]
l2norm: 1.297 [1.101, 1.493]

Parameterization:
x1: 0.3515473213046789
x2: 0.8443149905651808
x3: 0.19160807132720947
x4: 0.6976685579866171
x5: 0.3130832966417074
x6: 0.29660944268107414", "Arm 3_0

hartmann6: -0.194 [-0.390, 0.002]
l2norm: 1.256 [1.060, 1.452]

Parameterization:
x1: 0.8328361446037889
x2: 0.34940254129469395
x3: 0.23820482846349478
x4: 0.10947596561163664
x5: 0.00552850216627121
x6: 0.8229271983727813", "Arm 4_0

hartmann6: -0.21 [-0.406, -0.014]
l2norm: 1.236 [1.040, 1.432]

Parameterization:
x1: 0.5633540041744709
x2: 0.08204512856900692
x3: 0.6816800432279706
x4: 0.4190481761470437
x5: 0.32160758692771196
x6: 0.1490294188261032", "Arm 5_0

hartmann6: -0.182 [-0.378, 0.014]
l2norm: 1.971 [1.775, 2.167]

Parameterization:
x1: 0.9912177473306656
x2: 0.7120458632707596
x3: 0.7524356190115213
x4: 0.8732989579439163
x5: 0.3240836262702942
x6: 0.9211306972429156", "Arm 6_0

hartmann6: -0.177 [-0.373, 0.019]
l2norm: 1.614 [1.418, 1.810]

Parameterization:
x1: 0.38034947495907545
x2: 0.9629529910162091
x3: 0.23862588964402676
x4: 0.03235820308327675
x5: 0.28495802357792854
x6: 0.9491747254505754", "Arm 7_0

hartmann6: 0.091 [-0.105, 0.287]
l2norm: 1.578 [1.382, 1.774]

Parameterization:
x1: 0.2086636694148183
x2: 0.8466906864196062
x3: 0.2670538108795881
x4: 0.9696813663467765
x5: 0.6881511164829135
x6: 0.6347249178215861", "Arm 8_0

hartmann6: 0.065 [-0.131, 0.261]
l2norm: 1.707 [1.511, 1.903]

Parameterization:
x1: 0.9467948917299509
x2: 0.012833517976105213
x3: 0.3255065372213721
x4: 0.7246358916163445
x5: 0.8915406223386526
x6: 0.8611323377117515", "Arm 9_0

hartmann6: -0.199 [-0.395, -0.003]
l2norm: 1.218 [1.022, 1.414]

Parameterization:
x1: 0.28542813565582037
x2: 0.2504664473235607
x3: 0.7806174894794822
x4: 0.3865578854456544
x5: 0.6642285473644733
x6: 0.2633742420002818", "Arm 10_0

hartmann6: 0.064 [-0.132, 0.260]
l2norm: 1.756 [1.560, 1.952]

Parameterization:
x1: 0.9896778333932161
x2: 0.5722117917612195
x3: 0.9753914186730981
x4: 0.558608309365809
x5: 0.022496508434414864
x6: 0.5212270701304078", "Arm 11_0

hartmann6: -0.667 [-0.863, -0.471]
l2norm: 1.335 [1.139, 1.531]

Parameterization:
x1: 0.6510352278128266
x2: 0.3646875051781535
x3: 0.08286836743354797
x4: 0.3537624878808856
x5: 0.39962858986109495
x6: 0.9668617714196444", "Arm 12_0

hartmann6: -0.863 [-1.059, -0.667]
l2norm: 0.967 [0.771, 1.163]

Parameterization:
x1: 0.2796454133543929
x2: 0.7493353247347657
x3: 0.15464106288418103
x4: 0.5812618297166667
x5: 0.2791596601398423
x6: 0.2955178618446068", "Arm 13_0

hartmann6: -1.236 [-1.432, -1.040]
l2norm: 1.124 [0.928, 1.320]

Parameterization:
x1: 0.3284616901109552
x2: 0.7942139840808863
x3: 0.17620980069860573
x4: 0.6341203014929103
x5: 0.3026438225465261
x6: 0.28112899782055195", "Arm 14_0

hartmann6: -1.536 [-1.732, -1.340]
l2norm: 1.122 [0.926, 1.318]

Parameterization:
x1: 0.3927653163635802
x2: 0.7972149199557343
x3: 0.1838901153263288
x4: 0.6342739267708013
x5: 0.3120272349560831
x6: 0.23232319874145183", "Arm 15_0

hartmann6: -1.687 [-1.883, -1.491]
l2norm: 1.277 [1.081, 1.473]

Parameterization:
x1: 0.44349305999574096
x2: 0.7838152361269712
x3: 0.16240262264519248
x4: 0.5955858960357328
x5: 0.29266657888448067
x6: 0.22274509779224028", "Arm 16_0

hartmann6: -1.984 [-2.180, -1.788]
l2norm: 1.024 [0.828, 1.220]

Parameterization:
x1: 0.4322420347303606
x2: 0.736396129262977
x3: 0.1981840926303725
x4: 0.5791478799937887
x5: 0.3171316681641761
x6: 0.16913829009741782", "Arm 17_0

hartmann6: -2.349 [-2.545, -2.153]
l2norm: 1.208 [1.012, 1.404]

Parameterization:
x1: 0.46154941022051466
x2: 0.7222448880707345
x3: 0.2222531627655439
x4: 0.5871521350042745
x5: 0.33540777912229186
x6: 0.10296516044534137", "Arm 18_0

hartmann6: -2.427 [-2.623, -2.231]
l2norm: 1.107 [0.911, 1.303]

Parameterization:
x1: 0.4899263274204243
x2: 0.7210807707048381
x3: 0.22689470600158096
x4: 0.5387197872939041
x5: 0.34540695707077257
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hartmann6: -0.132 [-0.326, 0.061]
l2norm: 1.261 [1.080, 1.443]

Parameterization:
x1: 0.02089630253612995
x2: 0.9049676060676575
x3: 0.00016842130571603775
x4: 0.49008020758628845
x5: 0.1943160742521286
x6: 0.6511437296867371", "Arm 1_0

hartmann6: -0.067 [-0.260, 0.126]
l2norm: 0.945 [0.764, 1.127]

Parameterization:
x1: 0.2549036853015423
x2: 0.2767183566465974
x3: 0.5683933552354574
x4: 0.1376255163922906
x5: 0.39132768474519253
x6: 0.024703498929739", "Arm 2_0

hartmann6: -1.191 [-1.360, -1.022]
l2norm: 1.246 [1.110, 1.382]

Parameterization:
x1: 0.3515473213046789
x2: 0.8443149905651808
x3: 0.19160807132720947
x4: 0.6976685579866171
x5: 0.3130832966417074
x6: 0.29660944268107414", "Arm 3_0

hartmann6: -0.199 [-0.393, -0.005]
l2norm: 1.278 [1.095, 1.461]

Parameterization:
x1: 0.8328361446037889
x2: 0.34940254129469395
x3: 0.23820482846349478
x4: 0.10947596561163664
x5: 0.00552850216627121
x6: 0.8229271983727813", "Arm 4_0

hartmann6: -0.212 [-0.405, -0.018]
l2norm: 1.24 [1.059, 1.422]

Parameterization:
x1: 0.5633540041744709
x2: 0.08204512856900692
x3: 0.6816800432279706
x4: 0.4190481761470437
x5: 0.32160758692771196
x6: 0.1490294188261032", "Arm 5_0

hartmann6: -0.183 [-0.377, 0.010]
l2norm: 1.921 [1.738, 2.105]

Parameterization:
x1: 0.9912177473306656
x2: 0.7120458632707596
x3: 0.7524356190115213
x4: 0.8732989579439163
x5: 0.3240836262702942
x6: 0.9211306972429156", "Arm 6_0

hartmann6: -0.181 [-0.374, 0.013]
l2norm: 1.586 [1.402, 1.770]

Parameterization:
x1: 0.38034947495907545
x2: 0.9629529910162091
x3: 0.23862588964402676
x4: 0.03235820308327675
x5: 0.28495802357792854
x6: 0.9491747254505754", "Arm 7_0

hartmann6: 0.078 [-0.115, 0.272]
l2norm: 1.561 [1.377, 1.744]

Parameterization:
x1: 0.2086636694148183
x2: 0.8466906864196062
x3: 0.2670538108795881
x4: 0.9696813663467765
x5: 0.6881511164829135
x6: 0.6347249178215861", "Arm 8_0

hartmann6: 0.056 [-0.138, 0.249]
l2norm: 1.68 [1.496, 1.865]

Parameterization:
x1: 0.9467948917299509
x2: 0.012833517976105213
x3: 0.3255065372213721
x4: 0.7246358916163445
x5: 0.8915406223386526
x6: 0.8611323377117515", "Arm 9_0

hartmann6: -0.2 [-0.393, -0.006]
l2norm: 1.22 [1.039, 1.402]

Parameterization:
x1: 0.28542813565582037
x2: 0.2504664473235607
x3: 0.7806174894794822
x4: 0.3865578854456544
x5: 0.6642285473644733
x6: 0.2633742420002818", "Arm 10_0

hartmann6: 0.055 [-0.139, 0.249]
l2norm: 1.732 [1.548, 1.915]

Parameterization:
x1: 0.9896778333932161
x2: 0.5722117917612195
x3: 0.9753914186730981
x4: 0.558608309365809
x5: 0.022496508434414864
x6: 0.5212270701304078", "Arm 11_0

hartmann6: -0.656 [-0.849, -0.462]
l2norm: 1.345 [1.163, 1.528]

Parameterization:
x1: 0.6510352278128266
x2: 0.3646875051781535
x3: 0.08286836743354797
x4: 0.3537624878808856
x5: 0.39962858986109495
x6: 0.9668617714196444", "Arm 12_0

hartmann6: -0.907 [-1.083, -0.731]
l2norm: 1.043 [0.901, 1.185]

Parameterization:
x1: 0.2796454133543929
x2: 0.7493353247347657
x3: 0.15464106288418103
x4: 0.5812618297166667
x5: 0.2791596601398423
x6: 0.2955178618446068", "Arm 13_0

hartmann6: -1.184 [-1.309, -1.060]
l2norm: 1.133 [1.033, 1.232]

Parameterization:
x1: 0.3284616901109552
x2: 0.7942139840808863
x3: 0.17620980069860573
x4: 0.6341203014929103
x5: 0.3026438225465261
x6: 0.28112899782055195", "Arm 14_0

hartmann6: -1.569 [-1.697, -1.441]
l2norm: 1.172 [1.079, 1.264]

Parameterization:
x1: 0.3927653163635802
x2: 0.7972149199557343
x3: 0.1838901153263288
x4: 0.6342739267708013
x5: 0.3120272349560831
x6: 0.23232319874145183", "Arm 15_0

hartmann6: -1.685 [-1.850, -1.521]
l2norm: 1.174 [1.059, 1.289]

Parameterization:
x1: 0.44349305999574096
x2: 0.7838152361269712
x3: 0.16240262264519248
x4: 0.5955858960357328
x5: 0.29266657888448067
x6: 0.22274509779224028", "Arm 16_0

hartmann6: -1.993 [-2.132, -1.855]
l2norm: 1.119 [1.023, 1.216]

Parameterization:
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x3: 0.1981840926303725
x4: 0.5791478799937887
x5: 0.3171316681641761
x6: 0.16913829009741782", "Arm 17_0

hartmann6: -2.303 [-2.445, -2.161]
l2norm: 1.143 [1.032, 1.255]

Parameterization:
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x3: 0.2222531627655439
x4: 0.5871521350042745
x5: 0.33540777912229186
x6: 0.10296516044534137", "Arm 18_0

hartmann6: -2.398 [-2.570, -2.226]
l2norm: 1.142 [1.003, 1.281]

Parameterization:
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hartmann6: -0.13 [-0.326, 0.066]
l2norm: 1.251 [1.055, 1.447]

Parameterization:
x1: 0.02089630253612995
x2: 0.9049676060676575
x3: 0.00016842130571603775
x4: 0.49008020758628845
x5: 0.1943160742521286
x6: 0.6511437296867371", "Arm 1_0

hartmann6: -0.056 [-0.252, 0.140]
l2norm: 0.892 [0.696, 1.088]

Parameterization:
x1: 0.2549036853015423
x2: 0.2767183566465974
x3: 0.5683933552354574
x4: 0.1376255163922906
x5: 0.39132768474519253
x6: 0.024703498929739", "Arm 2_0

hartmann6: -1.195 [-1.391, -0.999]
l2norm: 1.297 [1.101, 1.493]

Parameterization:
x1: 0.3515473213046789
x2: 0.8443149905651808
x3: 0.19160807132720947
x4: 0.6976685579866171
x5: 0.3130832966417074
x6: 0.29660944268107414", "Arm 3_0

hartmann6: -0.194 [-0.390, 0.002]
l2norm: 1.256 [1.060, 1.452]

Parameterization:
x1: 0.8328361446037889
x2: 0.34940254129469395
x3: 0.23820482846349478
x4: 0.10947596561163664
x5: 0.00552850216627121
x6: 0.8229271983727813", "Arm 4_0

hartmann6: -0.21 [-0.406, -0.014]
l2norm: 1.236 [1.040, 1.432]

Parameterization:
x1: 0.5633540041744709
x2: 0.08204512856900692
x3: 0.6816800432279706
x4: 0.4190481761470437
x5: 0.32160758692771196
x6: 0.1490294188261032", "Arm 5_0

hartmann6: -0.182 [-0.378, 0.014]
l2norm: 1.971 [1.775, 2.167]

Parameterization:
x1: 0.9912177473306656
x2: 0.7120458632707596
x3: 0.7524356190115213
x4: 0.8732989579439163
x5: 0.3240836262702942
x6: 0.9211306972429156", "Arm 6_0

hartmann6: -0.177 [-0.373, 0.019]
l2norm: 1.614 [1.418, 1.810]

Parameterization:
x1: 0.38034947495907545
x2: 0.9629529910162091
x3: 0.23862588964402676
x4: 0.03235820308327675
x5: 0.28495802357792854
x6: 0.9491747254505754", "Arm 7_0

hartmann6: 0.091 [-0.105, 0.287]
l2norm: 1.578 [1.382, 1.774]

Parameterization:
x1: 0.2086636694148183
x2: 0.8466906864196062
x3: 0.2670538108795881
x4: 0.9696813663467765
x5: 0.6881511164829135
x6: 0.6347249178215861", "Arm 8_0

hartmann6: 0.065 [-0.131, 0.261]
l2norm: 1.707 [1.511, 1.903]

Parameterization:
x1: 0.9467948917299509
x2: 0.012833517976105213
x3: 0.3255065372213721
x4: 0.7246358916163445
x5: 0.8915406223386526
x6: 0.8611323377117515", "Arm 9_0

hartmann6: -0.199 [-0.395, -0.003]
l2norm: 1.218 [1.022, 1.414]

Parameterization:
x1: 0.28542813565582037
x2: 0.2504664473235607
x3: 0.7806174894794822
x4: 0.3865578854456544
x5: 0.6642285473644733
x6: 0.2633742420002818", "Arm 10_0

hartmann6: 0.064 [-0.132, 0.260]
l2norm: 1.756 [1.560, 1.952]

Parameterization:
x1: 0.9896778333932161
x2: 0.5722117917612195
x3: 0.9753914186730981
x4: 0.558608309365809
x5: 0.022496508434414864
x6: 0.5212270701304078", "Arm 11_0

hartmann6: -0.667 [-0.863, -0.471]
l2norm: 1.335 [1.139, 1.531]

Parameterization:
x1: 0.6510352278128266
x2: 0.3646875051781535
x3: 0.08286836743354797
x4: 0.3537624878808856
x5: 0.39962858986109495
x6: 0.9668617714196444", "Arm 12_0

hartmann6: -0.863 [-1.059, -0.667]
l2norm: 0.967 [0.771, 1.163]

Parameterization:
x1: 0.2796454133543929
x2: 0.7493353247347657
x3: 0.15464106288418103
x4: 0.5812618297166667
x5: 0.2791596601398423
x6: 0.2955178618446068", "Arm 13_0

hartmann6: -1.236 [-1.432, -1.040]
l2norm: 1.124 [0.928, 1.320]

Parameterization:
x1: 0.3284616901109552
x2: 0.7942139840808863
x3: 0.17620980069860573
x4: 0.6341203014929103
x5: 0.3026438225465261
x6: 0.28112899782055195", "Arm 14_0

hartmann6: -1.536 [-1.732, -1.340]
l2norm: 1.122 [0.926, 1.318]

Parameterization:
x1: 0.3927653163635802
x2: 0.7972149199557343
x3: 0.1838901153263288
x4: 0.6342739267708013
x5: 0.3120272349560831
x6: 0.23232319874145183", "Arm 15_0

hartmann6: -1.687 [-1.883, -1.491]
l2norm: 1.277 [1.081, 1.473]

Parameterization:
x1: 0.44349305999574096
x2: 0.7838152361269712
x3: 0.16240262264519248
x4: 0.5955858960357328
x5: 0.29266657888448067
x6: 0.22274509779224028", "Arm 16_0

hartmann6: -1.984 [-2.180, -1.788]
l2norm: 1.024 [0.828, 1.220]

Parameterization:
x1: 0.4322420347303606
x2: 0.736396129262977
x3: 0.1981840926303725
x4: 0.5791478799937887
x5: 0.3171316681641761
x6: 0.16913829009741782", "Arm 17_0

hartmann6: -2.349 [-2.545, -2.153]
l2norm: 1.208 [1.012, 1.404]

Parameterization:
x1: 0.46154941022051466
x2: 0.7222448880707345
x3: 0.2222531627655439
x4: 0.5871521350042745
x5: 0.33540777912229186
x6: 0.10296516044534137", "Arm 18_0

hartmann6: -2.427 [-2.623, -2.231]
l2norm: 1.107 [0.911, 1.303]

Parameterization:
x1: 0.4899263274204243
x2: 0.7210807707048381
x3: 0.22689470600158096
x4: 0.5387197872939041
x5: 0.34540695707077257
x6: 0.04900352968845858" ], [ "Arm 0_0

hartmann6: -0.132 [-0.326, 0.061]
l2norm: 1.261 [1.080, 1.443]

Parameterization:
x1: 0.02089630253612995
x2: 0.9049676060676575
x3: 0.00016842130571603775
x4: 0.49008020758628845
x5: 0.1943160742521286
x6: 0.6511437296867371", "Arm 1_0

hartmann6: -0.067 [-0.260, 0.126]
l2norm: 0.945 [0.764, 1.127]

Parameterization:
x1: 0.2549036853015423
x2: 0.2767183566465974
x3: 0.5683933552354574
x4: 0.1376255163922906
x5: 0.39132768474519253
x6: 0.024703498929739", "Arm 2_0

hartmann6: -1.191 [-1.360, -1.022]
l2norm: 1.246 [1.110, 1.382]

Parameterization:
x1: 0.3515473213046789
x2: 0.8443149905651808
x3: 0.19160807132720947
x4: 0.6976685579866171
x5: 0.3130832966417074
x6: 0.29660944268107414", "Arm 3_0

hartmann6: -0.199 [-0.393, -0.005]
l2norm: 1.278 [1.095, 1.461]

Parameterization:
x1: 0.8328361446037889
x2: 0.34940254129469395
x3: 0.23820482846349478
x4: 0.10947596561163664
x5: 0.00552850216627121
x6: 0.8229271983727813", "Arm 4_0

hartmann6: -0.212 [-0.405, -0.018]
l2norm: 1.24 [1.059, 1.422]

Parameterization:
x1: 0.5633540041744709
x2: 0.08204512856900692
x3: 0.6816800432279706
x4: 0.4190481761470437
x5: 0.32160758692771196
x6: 0.1490294188261032", "Arm 5_0

hartmann6: -0.183 [-0.377, 0.010]
l2norm: 1.921 [1.738, 2.105]

Parameterization:
x1: 0.9912177473306656
x2: 0.7120458632707596
x3: 0.7524356190115213
x4: 0.8732989579439163
x5: 0.3240836262702942
x6: 0.9211306972429156", "Arm 6_0

hartmann6: -0.181 [-0.374, 0.013]
l2norm: 1.586 [1.402, 1.770]

Parameterization:
x1: 0.38034947495907545
x2: 0.9629529910162091
x3: 0.23862588964402676
x4: 0.03235820308327675
x5: 0.28495802357792854
x6: 0.9491747254505754", "Arm 7_0

hartmann6: 0.078 [-0.115, 0.272]
l2norm: 1.561 [1.377, 1.744]

Parameterization:
x1: 0.2086636694148183
x2: 0.8466906864196062
x3: 0.2670538108795881
x4: 0.9696813663467765
x5: 0.6881511164829135
x6: 0.6347249178215861", "Arm 8_0

hartmann6: 0.056 [-0.138, 0.249]
l2norm: 1.68 [1.496, 1.865]

Parameterization:
x1: 0.9467948917299509
x2: 0.012833517976105213
x3: 0.3255065372213721
x4: 0.7246358916163445
x5: 0.8915406223386526
x6: 0.8611323377117515", "Arm 9_0

hartmann6: -0.2 [-0.393, -0.006]
l2norm: 1.22 [1.039, 1.402]

Parameterization:
x1: 0.28542813565582037
x2: 0.2504664473235607
x3: 0.7806174894794822
x4: 0.3865578854456544
x5: 0.6642285473644733
x6: 0.2633742420002818", "Arm 10_0

hartmann6: 0.055 [-0.139, 0.249]
l2norm: 1.732 [1.548, 1.915]

Parameterization:
x1: 0.9896778333932161
x2: 0.5722117917612195
x3: 0.9753914186730981
x4: 0.558608309365809
x5: 0.022496508434414864
x6: 0.5212270701304078", "Arm 11_0

hartmann6: -0.656 [-0.849, -0.462]
l2norm: 1.345 [1.163, 1.528]

Parameterization:
x1: 0.6510352278128266
x2: 0.3646875051781535
x3: 0.08286836743354797
x4: 0.3537624878808856
x5: 0.39962858986109495
x6: 0.9668617714196444", "Arm 12_0

hartmann6: -0.907 [-1.083, -0.731]
l2norm: 1.043 [0.901, 1.185]

Parameterization:
x1: 0.2796454133543929
x2: 0.7493353247347657
x3: 0.15464106288418103
x4: 0.5812618297166667
x5: 0.2791596601398423
x6: 0.2955178618446068", "Arm 13_0

hartmann6: -1.184 [-1.309, -1.060]
l2norm: 1.133 [1.033, 1.232]

Parameterization:
x1: 0.3284616901109552
x2: 0.7942139840808863
x3: 0.17620980069860573
x4: 0.6341203014929103
x5: 0.3026438225465261
x6: 0.28112899782055195", "Arm 14_0

hartmann6: -1.569 [-1.697, -1.441]
l2norm: 1.172 [1.079, 1.264]

Parameterization:
x1: 0.3927653163635802
x2: 0.7972149199557343
x3: 0.1838901153263288
x4: 0.6342739267708013
x5: 0.3120272349560831
x6: 0.23232319874145183", "Arm 15_0

hartmann6: -1.685 [-1.850, -1.521]
l2norm: 1.174 [1.059, 1.289]

Parameterization:
x1: 0.44349305999574096
x2: 0.7838152361269712
x3: 0.16240262264519248
x4: 0.5955858960357328
x5: 0.29266657888448067
x6: 0.22274509779224028", "Arm 16_0

hartmann6: -1.993 [-2.132, -1.855]
l2norm: 1.119 [1.023, 1.216]

Parameterization:
x1: 0.4322420347303606
x2: 0.736396129262977
x3: 0.1981840926303725
x4: 0.5791478799937887
x5: 0.3171316681641761
x6: 0.16913829009741782", "Arm 17_0

hartmann6: -2.303 [-2.445, -2.161]
l2norm: 1.143 [1.032, 1.255]

Parameterization:
x1: 0.46154941022051466
x2: 0.7222448880707345
x3: 0.2222531627655439
x4: 0.5871521350042745
x5: 0.33540777912229186
x6: 0.10296516044534137", "Arm 18_0

hartmann6: -2.398 [-2.570, -2.226]
l2norm: 1.142 [1.003, 1.281]

Parameterization:
x1: 0.4899263274204243
x2: 0.7210807707048381
x3: 0.22689470600158096
x4: 0.5387197872939041
x5: 0.34540695707077257
x6: 0.04900352968845858" ] ], "y": [ [ 1.2514953555017658, 0.8920526566896068, 1.2969049817719844, 1.2562548683173025, 1.2361996030734628, 1.9714240318579759, 1.6138959904441972, 1.5783277429193012, 1.7068242270010485, 1.2181918701920613, 1.7557314045546177, 1.3348751629943358, 0.9674964160805343, 1.124292907472836, 1.12245224042116, 1.2765563888396874, 1.0243704071861546, 1.2084493578270215, 1.1068572029223909 ], [ 1.2613477643262538, 0.9452143672046246, 1.2456030678671206, 1.2779798077863769, 1.240138344977189, 1.9214330331288514, 1.5862342098232318, 1.5607532527176127, 1.680306100397872, 1.220491489782588, 1.7317638592482565, 1.3452866754628805, 1.0428401271532017, 1.132502399557965, 1.171635337642292, 1.1740363853364495, 1.119480854642167, 1.1434652283616238, 1.1421390465127588 ] ] }, { "yaxis.title": "l2norm" } ], "label": "l2norm", "method": "update" } ], "x": 1.25, "xanchor": "left", "y": 0.72, "yanchor": "middle" } ], "width": 900, "xaxis": { "title": { "text": "hartmann6" }, "zeroline": true, "zerolinecolor": "red" }, "yaxis": { "title": { "text": "l2norm" }, "zeroline": true, "zerolinecolor": "red" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "render(plot_objective_vs_constraints(model, \"hartmann6\", rel=False))" ] }, { "cell_type": "markdown", "id": "a1e9f4f3", "metadata": { "originalKey": "f2d4fae3-2140-45d0-8142-49b91548ca59", "papermill": { "duration": 0.519966, "end_time": "2024-05-02T05:18:01.181663", "exception": false, "start_time": "2024-05-02T05:18:00.661697", "status": "completed" }, "tags": [] }, "source": [ "## 4. Cross-validation plots\n", "\n", "CV plots are useful to check how well the model predictions calibrate against the actual measurements. If all points are close to the dashed line, then the model is a good predictor of the real data." ] }, { "cell_type": "code", "execution_count": 8, "id": "db6453d0", "metadata": { "execution": { "iopub.execute_input": "2024-05-02T05:18:02.255604Z", "iopub.status.busy": "2024-05-02T05:18:02.255321Z", "iopub.status.idle": "2024-05-02T05:18:02.464040Z", "shell.execute_reply": "2024-05-02T05:18:02.463357Z" }, "executionStartTime": 1627397871181, "executionStopTime": 1627397871526, "originalKey": "f770f8a9-466c-4fd2-b268-3a0d166482f3", "papermill": { "duration": 0.768522, "end_time": "2024-05-02T05:18:02.466055", "exception": false, "start_time": "2024-05-02T05:18:01.697533", "status": "completed" }, "requestMsgId": "d6242810-a316-4e2b-b9dd-dd4c56b725b7", "tags": [] }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "hoverinfo": "none", "line": { "color": "black", "dash": "dot", "width": 2 }, "mode": "lines", "showlegend": false, "type": "scatter", "visible": true, "x": [ 0.6224840879311884, 2.2409926006163943 ], "y": [ 0.6224840879311884, 2.2409926006163943 ] }, { "error_x": { "array": [ 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196, 0.196 ], "color": "rgba(128,177,211,0.4)", "type": "data" }, "error_y": { "array": [ 0.48605922841899846, 0.47882802756647774, 0.18898787516127746, 0.5125403731783236, 0.4818242541032637, 0.5291228953997282, 0.5339586534959329, 0.5201994741432124, 0.5460886538966786, 0.4769007431545247, 0.5269947487814088, 0.5039856650016603, 0.20566366830909547, 0.11516159929727807, 0.10460459844716159, 0.14203740072431384, 0.11075705856510043, 0.13537977434164555, 0.19660431926048663 ], "color": "rgba(128,177,211,0.4)", "type": "data" }, "hoverinfo": "text", "marker": { "color": "rgba(128,177,211,1)" }, "mode": "markers", "name": "In-sample", "showlegend": true, "text": [ "Arm 0_0

Actual Outcome: 1.251 [1.055, 1.447]
Predicted Outcome: 1.322 [0.836, 1.808]

Parameterization:
x1: 0.02089630253612995
x2: 0.9049676060676575
x3: 0.00016842130571603775
x4: 0.49008020758628845
x5: 0.1943160742521286
x6: 0.6511437296867371", "Arm 1_0

Actual Outcome: 0.892 [0.696, 1.088]
Predicted Outcome: 1.262 [0.784, 1.741]

Parameterization:
x1: 0.2549036853015423
x2: 0.2767183566465974
x3: 0.5683933552354574
x4: 0.1376255163922906
x5: 0.39132768474519253
x6: 0.024703498929739", "Arm 2_0

Actual Outcome: 1.297 [1.101, 1.493]
Predicted Outcome: 1.198 [1.009, 1.387]

Parameterization:
x1: 0.3515473213046789
x2: 0.8443149905651808
x3: 0.19160807132720947
x4: 0.6976685579866171
x5: 0.3130832966417074
x6: 0.29660944268107414", "Arm 3_0

Actual Outcome: 1.256 [1.060, 1.452]
Predicted Outcome: 1.427 [0.914, 1.939]

Parameterization:
x1: 0.8328361446037889
x2: 0.34940254129469395
x3: 0.23820482846349478
x4: 0.10947596561163664
x5: 0.00552850216627121
x6: 0.8229271983727813", "Arm 4_0

Actual Outcome: 1.236 [1.040, 1.432]
Predicted Outcome: 1.264 [0.782, 1.746]

Parameterization:
x1: 0.5633540041744709
x2: 0.08204512856900692
x3: 0.6816800432279706
x4: 0.4190481761470437
x5: 0.32160758692771196
x6: 0.1490294188261032", "Arm 5_0

Actual Outcome: 1.971 [1.775, 2.167]
Predicted Outcome: 1.557 [1.028, 2.086]

Parameterization:
x1: 0.9912177473306656
x2: 0.7120458632707596
x3: 0.7524356190115213
x4: 0.8732989579439163
x5: 0.3240836262702942
x6: 0.9211306972429156", "Arm 6_0

Actual Outcome: 1.614 [1.418, 1.810]
Predicted Outcome: 1.381 [0.847, 1.915]

Parameterization:
x1: 0.38034947495907545
x2: 0.9629529910162091
x3: 0.23862588964402676
x4: 0.03235820308327675
x5: 0.28495802357792854
x6: 0.9491747254505754", "Arm 7_0

Actual Outcome: 1.578 [1.382, 1.774]
Predicted Outcome: 1.437 [0.917, 1.957]

Parameterization:
x1: 0.2086636694148183
x2: 0.8466906864196062
x3: 0.2670538108795881
x4: 0.9696813663467765
x5: 0.6881511164829135
x6: 0.6347249178215861", "Arm 8_0

Actual Outcome: 1.707 [1.511, 1.903]
Predicted Outcome: 1.474 [0.928, 2.021]

Parameterization:
x1: 0.9467948917299509
x2: 0.012833517976105213
x3: 0.3255065372213721
x4: 0.7246358916163445
x5: 0.8915406223386526
x6: 0.8611323377117515", "Arm 9_0

Actual Outcome: 1.218 [1.022, 1.414]
Predicted Outcome: 1.234 [0.757, 1.711]

Parameterization:
x1: 0.28542813565582037
x2: 0.2504664473235607
x3: 0.7806174894794822
x4: 0.3865578854456544
x5: 0.6642285473644733
x6: 0.2633742420002818", "Arm 10_0

Actual Outcome: 1.756 [1.560, 1.952]
Predicted Outcome: 1.558 [1.031, 2.085]

Parameterization:
x1: 0.9896778333932161
x2: 0.5722117917612195
x3: 0.9753914186730981
x4: 0.558608309365809
x5: 0.022496508434414864
x6: 0.5212270701304078", "Arm 11_0

Actual Outcome: 1.335 [1.139, 1.531]
Predicted Outcome: 1.414 [0.910, 1.918]

Parameterization:
x1: 0.6510352278128266
x2: 0.3646875051781535
x3: 0.08286836743354797
x4: 0.3537624878808856
x5: 0.39962858986109495
x6: 0.9668617714196444", "Arm 12_0

Actual Outcome: 0.967 [0.771, 1.163]
Predicted Outcome: 1.126 [0.920, 1.331]

Parameterization:
x1: 0.2796454133543929
x2: 0.7493353247347657
x3: 0.15464106288418103
x4: 0.5812618297166667
x5: 0.2791596601398423
x6: 0.2955178618446068", "Arm 13_0

Actual Outcome: 1.124 [0.928, 1.320]
Predicted Outcome: 1.135 [1.020, 1.250]

Parameterization:
x1: 0.3284616901109552
x2: 0.7942139840808863
x3: 0.17620980069860573
x4: 0.6341203014929103
x5: 0.3026438225465261
x6: 0.28112899782055195", "Arm 14_0

Actual Outcome: 1.122 [0.926, 1.318]
Predicted Outcome: 1.186 [1.081, 1.290]

Parameterization:
x1: 0.3927653163635802
x2: 0.7972149199557343
x3: 0.1838901153263288
x4: 0.6342739267708013
x5: 0.3120272349560831
x6: 0.23232319874145183", "Arm 15_0

Actual Outcome: 1.277 [1.081, 1.473]
Predicted Outcome: 1.12 [0.978, 1.262]

Parameterization:
x1: 0.44349305999574096
x2: 0.7838152361269712
x3: 0.16240262264519248
x4: 0.5955858960357328
x5: 0.29266657888448067
x6: 0.22274509779224028", "Arm 16_0

Actual Outcome: 1.024 [0.828, 1.220]
Predicted Outcome: 1.15 [1.039, 1.261]

Parameterization:
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x3: 0.1981840926303725
x4: 0.5791478799937887
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Actual Outcome: 1.208 [1.012, 1.404]
Predicted Outcome: 1.112 [0.977, 1.248]

Parameterization:
x1: 0.46154941022051466
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x3: 0.2222531627655439
x4: 0.5871521350042745
x5: 0.33540777912229186
x6: 0.10296516044534137", "Arm 18_0

Actual Outcome: 1.107 [0.911, 1.303]
Predicted Outcome: 1.178 [0.981, 1.374]

Parameterization:
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Actual Outcome: -0.13 [-0.326, 0.066]
Predicted Outcome: -0.212 [-1.411, 0.987]

Parameterization:
x1: 0.02089630253612995
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Actual Outcome: -0.056 [-0.252, 0.140]
Predicted Outcome: -0.445 [-1.606, 0.717]

Parameterization:
x1: 0.2549036853015423
x2: 0.2767183566465974
x3: 0.5683933552354574
x4: 0.1376255163922906
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Actual Outcome: -1.195 [-1.391, -0.999]
Predicted Outcome: -1.181 [-1.513, -0.848]

Parameterization:
x1: 0.3515473213046789
x2: 0.8443149905651808
x3: 0.19160807132720947
x4: 0.6976685579866171
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Actual Outcome: -0.194 [-0.390, 0.002]
Predicted Outcome: -0.411 [-1.642, 0.820]

Parameterization:
x1: 0.8328361446037889
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Actual Outcome: -0.21 [-0.406, -0.014]
Predicted Outcome: -0.279 [-1.455, 0.898]

Parameterization:
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Actual Outcome: -0.182 [-0.378, 0.014]
Predicted Outcome: -0.244 [-1.504, 1.015]

Parameterization:
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Actual Outcome: -0.177 [-0.373, 0.019]
Predicted Outcome: -0.324 [-1.580, 0.932]

Parameterization:
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Actual Outcome: 0.091 [-0.105, 0.287]
Predicted Outcome: -0.415 [-1.653, 0.822]

Parameterization:
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x3: 0.2670538108795881
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Actual Outcome: 0.065 [-0.131, 0.261]
Predicted Outcome: -0.342 [-1.619, 0.934]

Parameterization:
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x3: 0.3255065372213721
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Actual Outcome: -0.199 [-0.395, -0.003]
Predicted Outcome: -0.218 [-1.400, 0.964]

Parameterization:
x1: 0.28542813565582037
x2: 0.2504664473235607
x3: 0.7806174894794822
x4: 0.3865578854456544
x5: 0.6642285473644733
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Actual Outcome: 0.064 [-0.132, 0.260]
Predicted Outcome: -0.298 [-1.556, 0.961]

Parameterization:
x1: 0.9896778333932161
x2: 0.5722117917612195
x3: 0.9753914186730981
x4: 0.558608309365809
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Actual Outcome: -0.667 [-0.863, -0.471]
Predicted Outcome: -0.237 [-1.457, 0.983]

Parameterization:
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x3: 0.08286836743354797
x4: 0.3537624878808856
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Actual Outcome: -0.863 [-1.059, -0.667]
Predicted Outcome: -1.087 [-1.484, -0.690]

Parameterization:
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Actual Outcome: -1.236 [-1.432, -1.040]
Predicted Outcome: -1.149 [-1.310, -0.988]

Parameterization:
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Actual Outcome: -1.536 [-1.732, -1.340]
Predicted Outcome: -1.594 [-1.762, -1.425]

Parameterization:
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Actual Outcome: -1.687 [-1.883, -1.491]
Predicted Outcome: -1.682 [-1.983, -1.382]

Parameterization:
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Actual Outcome: -1.984 [-2.180, -1.788]
Predicted Outcome: -2.003 [-2.199, -1.808]

Parameterization:
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Actual Outcome: -2.349 [-2.545, -2.153]
Predicted Outcome: -2.253 [-2.459, -2.047]

Parameterization:
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Actual Outcome: -2.427 [-2.623, -2.231]
Predicted Outcome: -2.3 [-2.658, -1.941]

Parameterization:
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cv_results = cross_validate(model)\n", "render(interact_cross_validation(cv_results))" ] }, { "cell_type": "markdown", "id": "cd58cea1", "metadata": { "originalKey": "40f8ee99-fee8-4fd9-9cff-a7aa230dd5ae", "papermill": { "duration": 0.518681, "end_time": "2024-05-02T05:18:03.510145", "exception": false, "start_time": "2024-05-02T05:18:02.991464", "status": "completed" }, "tags": [] }, "source": [ "## 5. Slice plots\n", "\n", "Slice plots show the metric outcome as a function of one parameter while fixing the others. They serve a similar function as contour plots." ] }, { "cell_type": "code", "execution_count": 9, "id": "8e5f7a6e", "metadata": { "execution": { "iopub.execute_input": "2024-05-02T05:18:04.559897Z", "iopub.status.busy": "2024-05-02T05:18:04.559603Z", "iopub.status.idle": "2024-05-02T05:18:04.635068Z", "shell.execute_reply": "2024-05-02T05:18:04.634407Z" }, "executionStartTime": 1627397880415, "executionStopTime": 1627397880572, "originalKey": "aed7c789-a024-48c6-86f7-502e571e298f", "papermill": { "duration": 0.604709, "end_time": "2024-05-02T05:18:04.636700", "exception": false, "start_time": "2024-05-02T05:18:04.031991", "status": "completed" }, "requestMsgId": "a7238d82-f6bb-441d-badc-673dedaa101e", "tags": [] }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "fill": "toself", "fillcolor": "rgba(128, 177, 211, 0.2)", "hoverinfo": "none", "line": { 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "render(plot_slice(model, \"x2\", \"hartmann6\"))" ] }, { "cell_type": "markdown", "id": "82cd490c", "metadata": { "originalKey": "4975848f-31d4-4ed0-976c-39e3b7474fb7", "papermill": { "duration": 0.522278, "end_time": "2024-05-02T05:18:05.686761", "exception": false, "start_time": "2024-05-02T05:18:05.164483", "status": "completed" }, "tags": [] }, "source": [ "## 6. Tile plots\n", "\n", "Tile plots are useful for viewing the effect of each arm." ] }, { "cell_type": "code", "execution_count": 10, "id": "e81ab61c", "metadata": { "execution": { "iopub.execute_input": "2024-05-02T05:18:06.741424Z", "iopub.status.busy": "2024-05-02T05:18:06.741013Z", "iopub.status.idle": "2024-05-02T05:18:06.846685Z", "shell.execute_reply": "2024-05-02T05:18:06.846015Z" }, "executionStartTime": 1627397890236, "executionStopTime": 1627397890496, "originalKey": "2ed10008-8adf-4ce2-8334-04a4f2a3e895", "papermill": { "duration": 0.634166, "end_time": "2024-05-02T05:18:06.848319", "exception": false, "start_time": "2024-05-02T05:18:06.214153", "status": "completed" }, "requestMsgId": "33b593e6-2ec8-4bc4-b6e3-6586ddfb15c5", "tags": [] }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "error_y": { "array": [ 0.19343249169064813, 0.19326879804970498, 0.1688540225921982, 0.19356198997513796, 0.19333570453285598, 0.19366972517626893, 0.19365607505379634, 0.19358551955498182, 0.1937295342076324, 0.1933617370132661, 0.1936667597251116, 0.193518484051673, 0.17577759753634378, 0.12447900379828426, 0.1278645120989339, 0.16418519654906036, 0.13847594760979515, 0.14201730445761915, 0.17193756040101876 ], "color": "rgba(128,177,211,0.4)", "type": "data" }, "hoverinfo": "text", "legendgroup": "In-sample", "marker": { "color": "rgba(128,177,211,1)" }, "mode": "markers", "name": "In-sample", "showlegend": true, "text": [ "Arm 0_0

hartmann6: -0.132 [-0.326, 0.061]

Parameterization:
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x3: 0.00016842130571603775
x4: 0.49008020758628845
x5: 0.1943160742521286
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hartmann6: -0.067 [-0.260, 0.126]

Parameterization:
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x2: 0.2767183566465974
x3: 0.5683933552354574
x4: 0.1376255163922906
x5: 0.39132768474519253
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hartmann6: -1.191 [-1.360, -1.022]

Parameterization:
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hartmann6: -0.199 [-0.393, -0.005]

Parameterization:
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x4: 0.10947596561163664
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hartmann6: -0.212 [-0.405, -0.018]

Parameterization:
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x4: 0.4190481761470437
x5: 0.32160758692771196
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hartmann6: -0.183 [-0.377, 0.010]

Parameterization:
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x4: 0.8732989579439163
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hartmann6: -0.181 [-0.374, 0.013]

Parameterization:
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x3: 0.23862588964402676
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x5: 0.28495802357792854
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hartmann6: 0.078 [-0.115, 0.272]

Parameterization:
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x3: 0.2670538108795881
x4: 0.9696813663467765
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hartmann6: 0.056 [-0.138, 0.249]

Parameterization:
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x2: 0.012833517976105213
x3: 0.3255065372213721
x4: 0.7246358916163445
x5: 0.8915406223386526
x6: 0.8611323377117515", "Arm 9_0

hartmann6: -0.2 [-0.393, -0.006]

Parameterization:
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x3: 0.7806174894794822
x4: 0.3865578854456544
x5: 0.6642285473644733
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hartmann6: 0.055 [-0.139, 0.249]

Parameterization:
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x2: 0.5722117917612195
x3: 0.9753914186730981
x4: 0.558608309365809
x5: 0.022496508434414864
x6: 0.5212270701304078", "Arm 11_0

hartmann6: -0.656 [-0.849, -0.462]

Parameterization:
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x2: 0.3646875051781535
x3: 0.08286836743354797
x4: 0.3537624878808856
x5: 0.39962858986109495
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hartmann6: -0.907 [-1.083, -0.731]

Parameterization:
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x3: 0.15464106288418103
x4: 0.5812618297166667
x5: 0.2791596601398423
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hartmann6: -1.184 [-1.309, -1.060]

Parameterization:
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x3: 0.17620980069860573
x4: 0.6341203014929103
x5: 0.3026438225465261
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hartmann6: -1.569 [-1.697, -1.441]

Parameterization:
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x2: 0.7972149199557343
x3: 0.1838901153263288
x4: 0.6342739267708013
x5: 0.3120272349560831
x6: 0.23232319874145183", "Arm 15_0

hartmann6: -1.685 [-1.850, -1.521]

Parameterization:
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x2: 0.7838152361269712
x3: 0.16240262264519248
x4: 0.5955858960357328
x5: 0.29266657888448067
x6: 0.22274509779224028", "Arm 16_0

hartmann6: -1.993 [-2.132, -1.855]

Parameterization:
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x3: 0.1981840926303725
x4: 0.5791478799937887
x5: 0.3171316681641761
x6: 0.16913829009741782", "Arm 17_0

hartmann6: -2.303 [-2.445, -2.161]

Parameterization:
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x3: 0.2222531627655439
x4: 0.5871521350042745
x5: 0.33540777912229186
x6: 0.10296516044534137", "Arm 18_0

hartmann6: -2.398 [-2.570, -2.226]

Parameterization:
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Parameterization:
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l2norm: 0.945 [0.764, 1.127]

Parameterization:
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l2norm: 1.246 [1.110, 1.382]

Parameterization:
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l2norm: 1.278 [1.095, 1.461]

Parameterization:
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l2norm: 1.24 [1.059, 1.422]

Parameterization:
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l2norm: 1.921 [1.738, 2.105]

Parameterization:
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l2norm: 1.586 [1.402, 1.770]

Parameterization:
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x3: 0.23862588964402676
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l2norm: 1.561 [1.377, 1.744]

Parameterization:
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l2norm: 1.68 [1.496, 1.865]

Parameterization:
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l2norm: 1.22 [1.039, 1.402]

Parameterization:
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l2norm: 1.732 [1.548, 1.915]

Parameterization:
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l2norm: 1.345 [1.163, 1.528]

Parameterization:
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l2norm: 1.043 [0.901, 1.185]

Parameterization:
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l2norm: 1.133 [1.033, 1.232]

Parameterization:
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l2norm: 1.172 [1.079, 1.264]

Parameterization:
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l2norm: 1.174 [1.059, 1.289]

Parameterization:
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l2norm: 1.119 [1.023, 1.216]

Parameterization:
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l2norm: 1.143 [1.032, 1.255]

Parameterization:
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Parameterization:
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"updatemenus": [ { "buttons": [ { "args": [ "visible", [ true, false ] ], "label": "hartmann6", "method": "restyle" }, { "args": [ "visible", [ false, true ] ], "label": "l2norm", "method": "restyle" } ], "x": 0.075, "xanchor": "left", "y": 1.1, "yanchor": "middle" } ], "xaxis": { "title": { "text": "Arm" }, "type": "category", "zeroline": false }, "yaxis": { "ticksuffix": "", "title": { "text": "Effect" }, "zeroline": true, "zerolinecolor": "red" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "render(interact_fitted(model, rel=False))" ] }, { "cell_type": "markdown", "id": "590d2953", "metadata": { "papermill": { "duration": 0.532092, "end_time": "2024-05-02T05:18:07.909415", "exception": false, "start_time": "2024-05-02T05:18:07.377323", "status": "completed" }, "tags": [] }, "source": [ "## Fix for plots that are not rendering\n", "\n", "In certain environments like Google Colab or remote setups, plots may not render. If this is the case, we recommend using the below workaround which overrides the default renderer in plotly. The below cell changes the renderer to \"jupyterlab\" for this tutorial, but you can find the right renderer for your use case by calling `pio.renderers`" ] }, { "cell_type": "code", "execution_count": 11, "id": "9fbde8e7", "metadata": { "execution": { "iopub.execute_input": "2024-05-02T05:18:09.025620Z", "iopub.status.busy": "2024-05-02T05:18:09.025331Z", "iopub.status.idle": "2024-05-02T05:18:09.669690Z", "shell.execute_reply": "2024-05-02T05:18:09.668990Z" }, "papermill": { "duration": 1.183777, "end_time": "2024-05-02T05:18:09.672637", "exception": false, "start_time": "2024-05-02T05:18:08.488860", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 05-02 05:18:09] ax.service.ax_client: Retrieving contour plot with parameter 'x1' on X-axis and 'x2' on Y-axis, for metric 'hartmann6'. Remaining parameters are affixed to the middle of their range.\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "autocolorscale": false, "autocontour": true, "colorbar": { "tickfont": { "size": 8 }, "ticksuffix": "", "x": 0.45, "y": 0.5 }, "colorscale": [ [ 0.0, "rgb(247,252,253)" ], [ 0.125, "rgb(229,245,249)" ], [ 0.25, "rgb(204,236,230)" ], [ 0.375, "rgb(153,216,201)" ], [ 0.5, "rgb(102,194,164)" ], [ 0.625, "rgb(65,174,118)" ], [ 0.75, "rgb(35,139,69)" ], [ 0.875, "rgb(0,109,44)" ], [ 1.0, "rgb(0,68,27)" ] ], "contours": { "coloring": "heatmap" }, "hoverinfo": "x+y+z", "ncontours": 25, "type": "contour", "x": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 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