{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Select Parameters with Cross Validation\n", "\n", "This notebook demonstrates how to select parameters of best fit for a sparse tensor decomposition model using a cross-validation strategy. \n", "\n", "Fitting a sparse tensor decomposition model requires tuning two key parameters: the number of components (rank) of the model, and the sparsity coefficient (lambda) applied to each mode of the model. These parameters are rarely known a priori, and instead must be inferred. We've developed a cross-validation protocol for selecting parameters of best fit. This protocol relies on measurement replicates to generate three replicate data tensors of equivalent shapes. These replicate data tensors can be used to calculate cross-validated sum of squared error (SSE) and factor match score (FMS) metrics that can be used to identify the parameters of best fit.\n", "\n", "We will first simulate data replicates by generating three identical simulated data tensors -- `rep_a`, `rep_b`, and `rep_c` -- with independent noise added to each tensor to simulate variation between replicates. Next we will identify the best fit number of components using cross validated SSE. Locking in this rank, we'll fine tune the best fit sparsity coefficient using cross validated FMS." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# imports\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import scipy\n", "import seaborn as sns\n", "import tensorly as tl\n", "import tlviz\n", "from barnacle import (\n", " SparseCP, \n", " visualize_3d_tensor, \n", " simulated_sparse_tensor, \n", ")\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Replicate A\n" ] }, { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "axis0=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# generate simulated data\n", "\n", "true_rank = 5\n", "true_shape = [20, 15, 10]\n", "true_densities = [.2, .4, .6]\n", "\n", "# re-seed simulated data until all factor matrices are full rank\n", "full_rank = False\n", "while not full_rank:\n", " # generate simulated tensor\n", " sim_tensor = simulated_sparse_tensor(\n", " shape=true_shape, \n", " rank=true_rank, \n", " densities=true_densities, \n", " factor_dist_list=[\n", " scipy.stats.uniform(loc=-1, scale=2), \n", " scipy.stats.uniform(), \n", " scipy.stats.uniform()\n", " ], \n", " random_state=9481\n", " )\n", " # check that all factors are full rank\n", " full_rank = np.all([np.linalg.matrix_rank(factor) == true_rank for factor in sim_tensor.factors])\n", "\n", "# create three replicates with the same core signal data tensor, and 100% independent noise added to each\n", "rep_a = sim_tensor.to_tensor(noise_level=1, sparse_noise=True, random_state=91891)\n", "rep_b = sim_tensor.to_tensor(noise_level=1, sparse_noise=True, random_state=7394)\n", "rep_c = sim_tensor.to_tensor(noise_level=1, sparse_noise=True, random_state=1597)\n", "\n", "# visualize replicates\n", "for i, rep in enumerate([rep_a, rep_b, rep_c]): \n", " fig = visualize_3d_tensor(\n", " rep,\n", " shell=False, \n", " midpoint=0, \n", " show_colorbar=True,\n", " label_axes=True, \n", " range_color=[-1, 1], \n", " opacity=1, \n", " )\n", " print('Replicate {}'.format({0:'A', 1:'B', 2:'C'}[i]))\n", " fig.show()\n", " " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fitting rank-1 models\n", "Fitting rank-2 models\n", "Fitting rank-3 models\n", "Fitting rank-4 models\n", "Fitting rank-5 models\n", "Fitting rank-6 models\n", "Fitting rank-7 models\n", "Fitting rank-8 models\n" ] }, { "data": { "text/html": [ "
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RankFitting ReplicateComparison ReplicateComparisonSSE
01AAfitting0.657666
11ABcross-validation0.707090
21ACcross-validation0.714235
31BAcross-validation0.674137
41BBfitting0.691348
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678BBfitting0.352665
688BCcross-validation0.648890
698CAcross-validation0.645520
708CBcross-validation0.646472
718CCfitting0.341968
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72 rows × 5 columns

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" ], "text/plain": [ " Rank Fitting Replicate Comparison Replicate Comparison SSE\n", "0 1 A A fitting 0.657666\n", "1 1 A B cross-validation 0.707090\n", "2 1 A C cross-validation 0.714235\n", "3 1 B A cross-validation 0.674137\n", "4 1 B B fitting 0.691348\n", ".. ... ... ... ... ...\n", "67 8 B B fitting 0.352665\n", "68 8 B C cross-validation 0.648890\n", "69 8 C A cross-validation 0.645520\n", "70 8 C B cross-validation 0.646472\n", "71 8 C C fitting 0.341968\n", "\n", "[72 rows x 5 columns]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# perform a cross-validated parameter search for the number of components (rank)\n", "# NOTE: this block of code takes a minute or two to run\n", "\n", "results = []\n", "for rank in np.arange(1, 9, 1):\n", " print(f'Fitting rank-{rank} models')\n", " # instantiate sparse cp model\n", " model = SparseCP(\n", " rank=rank, \n", " lambdas=[0, 0, 0],\n", " nonneg_modes=[1, 2], \n", " tol=1e-5, \n", " random_state=21158, \n", " n_initializations=5\n", " )\n", " # fit model to each replicate data tensor\n", " for i, fit_rep in enumerate([rep_a, rep_b, rep_c]):\n", " cp = model.fit_transform(fit_rep, verbose=0)\n", " # calculate cross-validated SSE against each held out replicate\n", " for j, comparison_rep in enumerate([rep_a, rep_b, rep_c]):\n", " if i == j: \n", " comparison = 'fitting'\n", " else:\n", " comparison = 'cross-validation'\n", " sse = tlviz.model_evaluation.relative_sse(cp, comparison_rep)\n", " results.append({\n", " 'Rank': rank, \n", " 'Fitting Replicate': {0:'A', 1:'B', 2:'C'}[i], \n", " 'Comparison Replicate': {0:'A', 1:'B', 2:'C'}[j], \n", " 'Comparison': comparison, \n", " 'SSE': sse\n", " })\n", "# compile results into DataFrame\n", "rank_results_df = pd.DataFrame(results)\n", "rank_results_df\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The minimum cross-validated SSE (0.56) corresponds to a rank of 5.\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# identify the rank of best fit\n", "\n", "# find the rank that corresponds to the minimum mean cross-validated SSE\n", "cv_sse_df = rank_results_df[rank_results_df.Comparison == 'cross-validation'].groupby('Rank').mean('SSE')\n", "minimum = cv_sse_df.reset_index().sort_values('SSE').iloc[0, :]\n", "print(f'The minimum cross-validated SSE ({minimum.SSE:.2f}) corresponds to a rank of {int(minimum.Rank)}.')\n", "\n", "# visualize cross-validation data\n", "ax = sns.lineplot(\n", " rank_results_df, \n", " x='Rank', \n", " y='SSE', \n", " hue='Comparison', \n", " errorbar='se',\n", " err_style='bars'\n", ")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The cross-validation result reveal a clear minimum in cross-validated SSE that corresponds to a rank of 5. This indicates that the model of best fit should be parameterized with 5 components. However, this parameterization was done in the absence of any sparsity parameter (lambda=0). So fixing the number of components at 5, we next perform a similar cross-validated parameter search of sparsity coefficients to identify the ideal sparsity level for the model." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fitting models with sparsity coefficient of 0.05\n", "Fitting models with sparsity coefficient of 0.1\n", "Fitting models with sparsity coefficient of 0.2\n", "Fitting models with sparsity coefficient of 0.3\n", "Fitting models with sparsity coefficient of 0.4\n", "Fitting models with sparsity coefficient of 0.5\n", "Fitting models with sparsity coefficient of 0.6\n", "Fitting models with sparsity coefficient of 0.8\n", "Fitting models with sparsity coefficient of 1.0\n" ] }, { "data": { "text/html": [ "
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Sparsity CoefficientFitting ReplicateComparison ReplicateSSEFMS
00.05AB0.5636780.621984
10.05AC0.5759910.587359
20.05BA0.573267NaN
30.05BC0.5612550.665616
40.05CA0.549828NaN
50.05CB0.543003NaN
60.10AB0.5694680.621996
70.10AC0.5633500.559078
80.10BA0.553518NaN
90.10BC0.5686330.580420
100.10CA0.546041NaN
110.10CB0.538591NaN
120.20AB0.5655810.601660
130.20AC0.5583820.559783
140.20BA0.542834NaN
150.20BC0.5339840.773011
160.20CA0.544073NaN
170.20CB0.534930NaN
180.30AB0.5645860.603628
190.30AC0.5589940.558960
200.30BA0.540832NaN
210.30BC0.5323310.783579
220.30CA0.544599NaN
230.30CB0.534873NaN
240.40AB0.5674220.601039
250.40AC0.5623920.555470
260.40BA0.541534NaN
270.40BC0.5336580.789679
280.40CA0.548292NaN
290.40CB0.537406NaN
300.50AB0.5717220.590569
310.50AC0.5674950.550812
320.50BA0.549326NaN
330.50BC0.5653890.619288
340.50CA0.554570NaN
350.50CB0.542781NaN
360.60AB0.5774660.577193
370.60AC0.5741940.542921
380.60BA0.555087NaN
390.60BC0.5707690.620740
400.60CA0.561618NaN
410.60CB0.549689NaN
420.80AB0.5940290.437480
430.80AC0.5927810.523104
440.80BA0.606608NaN
450.80BC0.6171700.465549
460.80CA0.577298NaN
470.80CB0.566667NaN
481.00AB0.6352310.313387
491.00AC0.6364940.521444
501.00BA0.627666NaN
511.00BC0.6396010.454012
521.00CA0.597917NaN
531.00CB0.590343NaN
\n", "
" ], "text/plain": [ " Sparsity Coefficient Fitting Replicate Comparison Replicate SSE \\\n", "0 0.05 A B 0.563678 \n", "1 0.05 A C 0.575991 \n", "2 0.05 B A 0.573267 \n", "3 0.05 B C 0.561255 \n", "4 0.05 C A 0.549828 \n", "5 0.05 C B 0.543003 \n", "6 0.10 A B 0.569468 \n", "7 0.10 A C 0.563350 \n", "8 0.10 B A 0.553518 \n", "9 0.10 B C 0.568633 \n", "10 0.10 C A 0.546041 \n", "11 0.10 C B 0.538591 \n", "12 0.20 A B 0.565581 \n", "13 0.20 A C 0.558382 \n", "14 0.20 B A 0.542834 \n", "15 0.20 B C 0.533984 \n", "16 0.20 C A 0.544073 \n", "17 0.20 C B 0.534930 \n", "18 0.30 A B 0.564586 \n", "19 0.30 A C 0.558994 \n", "20 0.30 B A 0.540832 \n", "21 0.30 B C 0.532331 \n", "22 0.30 C A 0.544599 \n", "23 0.30 C B 0.534873 \n", "24 0.40 A B 0.567422 \n", "25 0.40 A C 0.562392 \n", "26 0.40 B A 0.541534 \n", "27 0.40 B C 0.533658 \n", "28 0.40 C A 0.548292 \n", "29 0.40 C B 0.537406 \n", "30 0.50 A B 0.571722 \n", "31 0.50 A C 0.567495 \n", "32 0.50 B A 0.549326 \n", "33 0.50 B C 0.565389 \n", "34 0.50 C A 0.554570 \n", "35 0.50 C B 0.542781 \n", "36 0.60 A B 0.577466 \n", "37 0.60 A C 0.574194 \n", "38 0.60 B A 0.555087 \n", "39 0.60 B C 0.570769 \n", "40 0.60 C A 0.561618 \n", "41 0.60 C B 0.549689 \n", "42 0.80 A B 0.594029 \n", "43 0.80 A C 0.592781 \n", "44 0.80 B A 0.606608 \n", "45 0.80 B C 0.617170 \n", "46 0.80 C A 0.577298 \n", "47 0.80 C B 0.566667 \n", "48 1.00 A B 0.635231 \n", "49 1.00 A C 0.636494 \n", "50 1.00 B A 0.627666 \n", "51 1.00 B C 0.639601 \n", "52 1.00 C A 0.597917 \n", "53 1.00 C B 0.590343 \n", "\n", " FMS \n", "0 0.621984 \n", "1 0.587359 \n", "2 NaN \n", "3 0.665616 \n", "4 NaN \n", "5 NaN \n", "6 0.621996 \n", "7 0.559078 \n", "8 NaN \n", "9 0.580420 \n", "10 NaN \n", "11 NaN \n", "12 0.601660 \n", "13 0.559783 \n", "14 NaN \n", "15 0.773011 \n", "16 NaN \n", "17 NaN \n", "18 0.603628 \n", "19 0.558960 \n", "20 NaN \n", "21 0.783579 \n", "22 NaN \n", "23 NaN \n", "24 0.601039 \n", "25 0.555470 \n", "26 NaN \n", "27 0.789679 \n", "28 NaN \n", "29 NaN \n", "30 0.590569 \n", "31 0.550812 \n", "32 NaN \n", "33 0.619288 \n", "34 NaN \n", "35 NaN \n", "36 0.577193 \n", "37 0.542921 \n", "38 NaN \n", "39 0.620740 \n", "40 NaN \n", "41 NaN \n", "42 0.437480 \n", "43 0.523104 \n", "44 NaN \n", "45 0.465549 \n", "46 NaN \n", "47 NaN \n", "48 0.313387 \n", "49 0.521444 \n", "50 NaN \n", "51 0.454012 \n", "52 NaN \n", "53 NaN " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# perform a cross-validated parameter search for the sparsity coefficient\n", "# NOTE: this block of code takes a minute or two to run\n", "\n", "# define range of lambda values to test\n", "lambdas = [0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.]\n", "\n", "results = []\n", "for lamb in lambdas:\n", " print(f'Fitting models with sparsity coefficient of {lamb}')\n", " # instantiate sparse cp model\n", " model = SparseCP(\n", " rank=5, \n", " lambdas=[lamb, 0, 0],\n", " nonneg_modes=[1, 2], \n", " tol=1e-5, \n", " random_state=21158, \n", " n_initializations=5\n", " )\n", " # fit model to each replicate data tensor\n", " fit_models = []\n", " for i, fit_rep in enumerate([rep_a, rep_b, rep_c]):\n", " cp = model.fit_transform(fit_rep, verbose=0)\n", " fit_models.append(cp)\n", " # calculate cross-validated FMS and SSE between each pair of replicates\n", " for i, fit_rep in enumerate([rep_a, rep_b, rep_c]):\n", " for j, comparison_rep in enumerate([rep_a, rep_b, rep_c]):\n", " if i == j: \n", " continue # only compute cross-validated metrics\n", " elif i < j:\n", " fms = tlviz.factor_tools.factor_match_score(fit_models[i], fit_models[j])\n", " else:\n", " fms = np.nan # FMS is symmetrical, so FMS(A, B) == FMS(B, A)\n", " sse = tlviz.model_evaluation.relative_sse(fit_models[i], comparison_rep)\n", " results.append({\n", " 'Sparsity Coefficient': lamb, \n", " 'Fitting Replicate': {0:'A', 1:'B', 2:'C'}[i], \n", " 'Comparison Replicate': {0:'A', 1:'B', 2:'C'}[j], \n", " 'SSE': sse, \n", " 'FMS': fms\n", " })\n", "# compile results into DataFrame\n", "lambda_results_df = pd.DataFrame(results)\n", "lambda_results_df\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The minimum cross-validated SSE (0.55) corresponds to a sparsity coefficient of 0.3.\n", "The maximum cross-validated FMS (0.65) corresponds to a sparsity coefficient of 0.4.\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# identify the sparsity coefficient of best fit\n", "\n", "# find the lambda that corresponds to the minimum mean cross-validated SSE\n", "cv_df = lambda_results_df.groupby('Sparsity Coefficient').mean(['SSE', 'FMS']).reset_index()\n", "min_sse = cv_df.sort_values('SSE').iloc[0, :]\n", "print(f\"The minimum cross-validated SSE ({min_sse.SSE:.2f}) \" + \n", " f\"corresponds to a sparsity coefficient of {min_sse['Sparsity Coefficient']}.\")\n", "\n", "# find the lambda that corresponds to the maximum mean cross-validated FMS\n", "cv_df = lambda_results_df.groupby('Sparsity Coefficient').mean(['SSE', 'FMS']).reset_index()\n", "max_fms = cv_df.sort_values('FMS', ascending=False).iloc[0, :]\n", "print(f\"The maximum cross-validated FMS ({max_fms.FMS:.2f}) \" + \n", " f\"corresponds to a sparsity coefficient of {max_fms['Sparsity Coefficient']}.\")\n", "\n", "# arrange data in tidy format for plotting\n", "plot_df = lambda_results_df.melt(\n", " id_vars=['Sparsity Coefficient', 'Fitting Replicate', 'Comparison Replicate'], \n", " value_vars=['SSE', 'FMS'], \n", " var_name='Metric', \n", " value_name='Score'\n", ")\n", "\n", "# visualize cross-validation data\n", "ax = sns.lineplot(\n", " plot_df, \n", " x='Sparsity Coefficient', \n", " y='Score',\n", " hue='Metric', \n", " errorbar='se',\n", " err_style='bars'\n", ")\n", "ax.set(xscale='log'); \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evidenced by these results, selecting the best sparsity coefficient is not always a straightforward task. However, in this example it is reassuring to see that the cross-validated SSE and FMS scores point to a similar range of sparsity coefficient values between 0.2 and 0.4. Above this range, there is a clear drop off in FMS and an increase in SSE, and below this range there is a similar trend that is subtler but nevertheless distinct. \n", "\n", "Within the indicated range, selecting the most appropriate sparsity coefficient probably depends on the intended application of the model. There are a number of hueristics that can help, such as the \"one standard error rule\" in which we select the sparsest model for which the cross-validated score remains within one standard error of the best overall score. In this example, this heuristic might lead to a selection of 0.4 as the sparsest model of best fit." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 4 }