source: trunk/sources/HeuristicLab.Algorithms.DataAnalysis/3.4/GradientBoostedTrees/RegressionTreeBuilder.cs @ 13992

Last change on this file since 13992 was 13992, checked in by gkronber, 3 years ago

#2604: set default target variable to string.Empty in AfterDeserialization hook for regression and classification models and changed a few ctor calls to correctly pass the target variable

File size: 19.8 KB
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1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2015 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
4 * and the BEACON Center for the Study of Evolution in Action.
5 *
6 * This file is part of HeuristicLab.
7 *
8 * HeuristicLab is free software: you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation, either version 3 of the License, or
11 * (at your option) any later version.
12 *
13 * HeuristicLab is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
16 * GNU General Public License for more details.
17 *
18 * You should have received a copy of the GNU General Public License
19 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
20 */
21#endregion
22
23using System;
24using System.Collections;
25using System.Collections.Generic;
26using System.Diagnostics;
27using System.Linq;
28using HeuristicLab.Core;
29using HeuristicLab.Problems.DataAnalysis;
30
31namespace HeuristicLab.Algorithms.DataAnalysis {
32  // This class implements a greedy decision tree learner which selects splits with the maximum reduction in sum of squared errors.
33  // The tree builder also tracks variable relevance metrics based on the splits and improvement after the split.
34  // The implementation is tuned for gradient boosting where multiple trees have to be calculated for the same training data
35  // each time with a different target vector. Vectors of idx to allow iteration of intput variables in sorted order are
36  // pre-calculated so that optimal thresholds for splits can be calculated in O(n) for each input variable.
37  // After each split the row idx are partitioned in a left an right part.
38  internal class RegressionTreeBuilder {
39    private readonly IRandom random;
40    private readonly IRegressionProblemData problemData;
41
42    private readonly int nCols;
43    private readonly double[][] x; // all training data (original order from problemData), x is constant
44    private double[] originalY; // the original target labels (from problemData), originalY is constant
45    private double[] curPred; // current predictions for originalY (in case we are using gradient boosting, otherwise = zeros), only necessary for line search
46
47    private double[] y; // training labels (original order from problemData), y can be changed
48
49    private Dictionary<string, double> sumImprovements; // for variable relevance calculation
50
51    private readonly string[] allowedVariables; // all variables in shuffled order
52    private Dictionary<string, int> varName2Index; // maps the variable names to column indexes
53    private int effectiveVars; // number of variables that are used from allowedVariables
54
55    private int effectiveRows; // number of rows that are used from
56    private readonly int[][] sortedIdxAll;
57    private readonly int[][] sortedIdx; // random selection from sortedIdxAll (for r < 1.0)
58
59    // helper arrays which are allocated to maximal necessary size only once in the ctor
60    private readonly int[] internalIdx, which, leftTmp, rightTmp;
61    private readonly double[] outx;
62    private readonly int[] outSortedIdx;
63
64    private RegressionTreeModel.TreeNode[] tree; // tree is represented as a flat array of nodes
65    private int curTreeNodeIdx; // the index where the next tree node is stored
66
67    // This class represents information about potential splits.
68    // For each node generated the best splitting variable and threshold as well as
69    // the improvement from the split are stored in a priority queue
70    private class PartitionSplits {
71      public int ParentNodeIdx { get; set; } // the idx of the leaf node representing this partition
72      public int StartIdx { get; set; } // the start idx of the partition
73      public int EndIndex { get; set; } // the end idx of the partition
74      public string SplittingVariable { get; set; } // the best splitting variable
75      public double SplittingThreshold { get; set; } // the best threshold
76      public double SplittingImprovement { get; set; } // the improvement of the split (for priority queue)
77    }
78
79    // this list hold partitions with the information about the best split (organized as a sorted queue)
80    private readonly IList<PartitionSplits> queue;
81
82    // prepare and allocate buffer variables in ctor
83    public RegressionTreeBuilder(IRegressionProblemData problemData, IRandom random) {
84      this.problemData = problemData;
85      this.random = random;
86
87      var rows = problemData.TrainingIndices.Count();
88
89      this.nCols = problemData.AllowedInputVariables.Count();
90
91      allowedVariables = problemData.AllowedInputVariables.ToArray();
92      varName2Index = new Dictionary<string, int>(allowedVariables.Length);
93      for (int i = 0; i < allowedVariables.Length; i++) varName2Index.Add(allowedVariables[i], i);
94
95      sortedIdxAll = new int[nCols][];
96      sortedIdx = new int[nCols][];
97      sumImprovements = new Dictionary<string, double>();
98      internalIdx = new int[rows];
99      which = new int[rows];
100      leftTmp = new int[rows];
101      rightTmp = new int[rows];
102      outx = new double[rows];
103      outSortedIdx = new int[rows];
104      queue = new List<PartitionSplits>(100);
105
106      x = new double[nCols][];
107      originalY = problemData.Dataset.GetDoubleValues(problemData.TargetVariable, problemData.TrainingIndices).ToArray();
108      y = new double[originalY.Length];
109      Array.Copy(originalY, y, y.Length); // copy values (originalY is fixed, y is changed in gradient boosting)
110      curPred = Enumerable.Repeat(0.0, y.Length).ToArray(); // zeros
111
112      int col = 0;
113      foreach (var inputVariable in problemData.AllowedInputVariables) {
114        x[col] = problemData.Dataset.GetDoubleValues(inputVariable, problemData.TrainingIndices).ToArray();
115        sortedIdxAll[col] = Enumerable.Range(0, rows).OrderBy(r => x[col][r]).ToArray();
116        sortedIdx[col] = new int[rows];
117        col++;
118      }
119    }
120
121    // specific interface that allows to specify the target labels and the training rows which is necessary when for gradient boosted trees
122    public IRegressionModel CreateRegressionTreeForGradientBoosting(double[] y, double[] curPred, int maxSize, int[] idx, ILossFunction lossFunction, double r = 0.5, double m = 0.5) {
123      Debug.Assert(maxSize > 0);
124      Debug.Assert(r > 0);
125      Debug.Assert(r <= 1.0);
126      Debug.Assert(y.Count() == this.y.Length);
127      Debug.Assert(m > 0);
128      Debug.Assert(m <= 1.0);
129
130      // y and curPred are changed in gradient boosting
131      this.y = y; 
132      this.curPred = curPred; 
133
134      // shuffle row idx
135      HeuristicLab.Random.ListExtensions.ShuffleInPlace(idx, random);
136
137      int nRows = idx.Count();
138
139      // shuffle variable names
140      HeuristicLab.Random.ListExtensions.ShuffleInPlace(allowedVariables, random);
141
142      // only select a part of the rows and columns randomly
143      effectiveRows = (int)Math.Ceiling(nRows * r);
144      effectiveVars = (int)Math.Ceiling(nCols * m);
145
146      // the which array is used for partitioing row idxs 
147      Array.Clear(which, 0, which.Length);
148
149      // mark selected rows
150      for (int row = 0; row < effectiveRows; row++) {
151        which[idx[row]] = 1; // we use the which vector as a temporary variable here
152        internalIdx[row] = idx[row];
153      }
154
155      for (int col = 0; col < nCols; col++) {
156        int i = 0;
157        for (int row = 0; row < nRows; row++) {
158          if (which[sortedIdxAll[col][row]] > 0) {
159            Debug.Assert(i < effectiveRows);
160            sortedIdx[col][i] = sortedIdxAll[col][row];
161            i++;
162          }
163        }
164      }
165
166      this.tree = new RegressionTreeModel.TreeNode[maxSize];
167      this.queue.Clear();
168      this.curTreeNodeIdx = 0;
169
170      // start out with only one leaf node (constant prediction)
171      // and calculate the best split for this root node and enqueue it into a queue sorted by improvement throught the split
172      // start and end idx are inclusive
173      CreateLeafNode(0, effectiveRows - 1, lossFunction);
174
175      // process the priority queue to complete the tree
176      CreateRegressionTreeFromQueue(maxSize, lossFunction);
177
178      return new RegressionTreeModel(tree.ToArray(), problemData.TargetVariable, );
179    }
180
181
182    // processes potential splits from the queue as long as splits are remaining and the maximum size of the tree is not reached
183    private void CreateRegressionTreeFromQueue(int maxNodes, ILossFunction lossFunction) {
184      while (queue.Any() && curTreeNodeIdx + 1 < maxNodes) { // two nodes are created in each loop
185        var f = queue[queue.Count - 1]; // last element has the largest improvement
186        queue.RemoveAt(queue.Count - 1);
187
188        var startIdx = f.StartIdx;
189        var endIdx = f.EndIndex;
190
191        Debug.Assert(endIdx - startIdx >= 0);
192        Debug.Assert(startIdx >= 0);
193        Debug.Assert(endIdx < internalIdx.Length);
194
195        // split partition into left and right
196        int splitIdx;
197        SplitPartition(f.StartIdx, f.EndIndex, f.SplittingVariable, f.SplittingThreshold, out splitIdx);
198        Debug.Assert(splitIdx + 1 <= endIdx);
199        Debug.Assert(startIdx <= splitIdx);
200
201        // create two leaf nodes (and enqueue best splits for both)
202        var leftTreeIdx = CreateLeafNode(startIdx, splitIdx, lossFunction);
203        var rightTreeIdx = CreateLeafNode(splitIdx + 1, endIdx, lossFunction);
204
205        // overwrite existing leaf node with an internal node
206        tree[f.ParentNodeIdx] = new RegressionTreeModel.TreeNode(f.SplittingVariable, f.SplittingThreshold, leftTreeIdx, rightTreeIdx, weightLeft: (splitIdx - startIdx + 1) / (double)(endIdx - startIdx + 1));
207      }
208    }
209
210
211    // returns the index of the newly created tree node
212    private int CreateLeafNode(int startIdx, int endIdx, ILossFunction lossFunction) {
213      // write a leaf node
214      var val = lossFunction.LineSearch(originalY, curPred, internalIdx, startIdx, endIdx);
215      tree[curTreeNodeIdx] = new RegressionTreeModel.TreeNode(RegressionTreeModel.TreeNode.NO_VARIABLE, val);
216
217      EnqueuePartitionSplit(curTreeNodeIdx, startIdx, endIdx);
218      curTreeNodeIdx++;
219      return curTreeNodeIdx - 1;
220    }
221
222
223    // calculates the optimal split for the partition [startIdx .. endIdx] (inclusive)
224    // which is represented by the leaf node with the specified nodeIdx
225    private void EnqueuePartitionSplit(int nodeIdx, int startIdx, int endIdx) {
226      double threshold, improvement;
227      string bestVariableName;
228      // only enqueue a new split if there are at least 2 rows left and a split is possible
229      if (startIdx < endIdx &&
230        FindBestVariableAndThreshold(startIdx, endIdx, out threshold, out bestVariableName, out improvement)) {
231        var split = new PartitionSplits() {
232          ParentNodeIdx = nodeIdx,
233          StartIdx = startIdx,
234          EndIndex = endIdx,
235          SplittingThreshold = threshold,
236          SplittingVariable = bestVariableName
237        };
238        InsertSortedQueue(split);
239      }
240    }
241
242
243    // routine for splitting a partition of rows stored in internalIdx between startIdx and endIdx into
244    // a left partition and a right partition using the given splittingVariable and threshold
245    // the splitIdx is the last index of the left partition
246    // splitIdx + 1 is the first index of the right partition
247    // startIdx and endIdx are inclusive
248    private void SplitPartition(int startIdx, int endIdx, string splittingVar, double threshold, out int splitIdx) {
249      int bestVarIdx = varName2Index[splittingVar];
250      // split - two pass
251
252      // store which index goes into which partition
253      for (int k = startIdx; k <= endIdx; k++) {
254        if (x[bestVarIdx][internalIdx[k]] <= threshold)
255          which[internalIdx[k]] = -1; // left partition
256        else
257          which[internalIdx[k]] = 1; // right partition
258      }
259
260      // partition sortedIdx for each variable
261      int i;
262      int j;
263      for (int col = 0; col < nCols; col++) {
264        i = 0;
265        j = 0;
266        int k;
267        for (k = startIdx; k <= endIdx; k++) {
268          Debug.Assert(Math.Abs(which[sortedIdx[col][k]]) == 1);
269
270          if (which[sortedIdx[col][k]] < 0) {
271            leftTmp[i++] = sortedIdx[col][k];
272          } else {
273            rightTmp[j++] = sortedIdx[col][k];
274          }
275        }
276        Debug.Assert(i > 0); // at least on element in the left partition
277        Debug.Assert(j > 0); // at least one element in the right partition
278        Debug.Assert(i + j == endIdx - startIdx + 1);
279        k = startIdx;
280        for (int l = 0; l < i; l++) sortedIdx[col][k++] = leftTmp[l];
281        for (int l = 0; l < j; l++) sortedIdx[col][k++] = rightTmp[l];
282      }
283
284      // partition row indices
285      i = startIdx;
286      j = endIdx;
287      while (i <= j) {
288        Debug.Assert(Math.Abs(which[internalIdx[i]]) == 1);
289        Debug.Assert(Math.Abs(which[internalIdx[j]]) == 1);
290        if (which[internalIdx[i]] < 0) i++;
291        else if (which[internalIdx[j]] > 0) j--;
292        else {
293          Debug.Assert(which[internalIdx[i]] > 0);
294          Debug.Assert(which[internalIdx[j]] < 0);
295          // swap
296          int tmp = internalIdx[i];
297          internalIdx[i] = internalIdx[j];
298          internalIdx[j] = tmp;
299          i++;
300          j--;
301        }
302      }
303      Debug.Assert(j + 1 == i);
304      Debug.Assert(i <= endIdx);
305      Debug.Assert(startIdx <= j);
306
307      splitIdx = j;
308    }
309
310    private bool FindBestVariableAndThreshold(int startIdx, int endIdx, out double threshold, out string bestVar, out double improvement) {
311      Debug.Assert(startIdx < endIdx + 1); // at least 2 elements
312
313      int rows = endIdx - startIdx + 1;
314      Debug.Assert(rows >= 2);
315
316      double sumY = 0.0;
317      for (int i = startIdx; i <= endIdx; i++) {
318        sumY += y[internalIdx[i]];
319      }
320
321      // see description of calculation in FindBestThreshold
322      double bestImprovement = 1.0 / rows * sumY * sumY; // any improvement must be larger than this baseline
323      double bestThreshold = double.PositiveInfinity;
324      bestVar = RegressionTreeModel.TreeNode.NO_VARIABLE;
325
326      for (int col = 0; col < effectiveVars; col++) {
327        // sort values for variable to prepare for threshold selection
328        var curVariable = allowedVariables[col];
329        var curVariableIdx = varName2Index[curVariable];
330        for (int i = startIdx; i <= endIdx; i++) {
331          var sortedI = sortedIdx[curVariableIdx][i];
332          outSortedIdx[i - startIdx] = sortedI;
333          outx[i - startIdx] = x[curVariableIdx][sortedI];
334        }
335
336        double curImprovement;
337        double curThreshold;
338        FindBestThreshold(outx, outSortedIdx, rows, y, sumY, out curThreshold, out curImprovement);
339
340        if (curImprovement > bestImprovement) {
341          bestImprovement = curImprovement;
342          bestThreshold = curThreshold;
343          bestVar = allowedVariables[col];
344        }
345      }
346      if (bestVar == RegressionTreeModel.TreeNode.NO_VARIABLE) {
347        // not successfull
348        threshold = double.PositiveInfinity;
349        improvement = double.NegativeInfinity;
350        return false;
351      } else {
352        UpdateVariableRelevance(bestVar, sumY, bestImprovement, rows);
353        improvement = bestImprovement;
354        threshold = bestThreshold;
355        return true;
356      }
357    }
358
359    // x [0..N-1] contains rows sorted values in the range from [0..rows-1]
360    // sortedIdx [0..N-1] contains the idx of the values in x in the original dataset in the range from [0..rows-1]
361    // rows specifies the number of valid entries in x and sortedIdx
362    // y [0..N-1] contains the target values in original sorting order
363    // sumY is y.Sum()
364    //
365    // the routine returns the best threshold (x[i] + x[i+1]) / 2 for i = [0 .. rows-2] by calculating the reduction in squared error
366    // additionally the reduction in squared error is returned in bestImprovement
367    // if all elements of x are equal the routing fails to produce a threshold
368    private static void FindBestThreshold(double[] x, int[] sortedIdx, int rows, double[] y, double sumY, out double bestThreshold, out double bestImprovement) {
369      Debug.Assert(rows >= 2);
370
371      double sl = 0.0;
372      double sr = sumY;
373      double nl = 0.0;
374      double nr = rows;
375
376      bestImprovement = 1.0 / rows * sumY * sumY; // this is the baseline for the improvement
377      bestThreshold = double.NegativeInfinity;
378      // for all thresholds
379      // if we have n rows there are n-1 possible splits
380      for (int i = 0; i < rows - 1; i++) {
381        sl += y[sortedIdx[i]];
382        sr -= y[sortedIdx[i]];
383
384        nl++;
385        nr--;
386        Debug.Assert(nl > 0);
387        Debug.Assert(nr > 0);
388
389        if (x[i] < x[i + 1]) { // don't try to split when two elements are equal
390
391          // goal is to find the split with leading to minimal total variance of left and right parts
392          // without partitioning the variance is var(y) = E(y²) - E(y)² 
393          //    = 1/n * sum(y²) - (1/n * sum(y))²
394          //      -------------   ---------------
395          //         constant       baseline for improvement
396          //
397          // if we split into right and left part the overall variance is the weigthed combination nl/n * var(y_l) + nr/n * var(y_r) 
398          //    = nl/n * (1/nl * sum(y_l²) - (1/nl * sum(y_l))²) + nr/n * (1/nr * sum(y_r²) - (1/nr * sum(y_r))²)
399          //    = 1/n * sum(y_l²) - 1/nl * 1/n * sum(y_l)² + 1/n * sum(y_r²) - 1/nr * 1/n * sum(y_r)²
400          //    = 1/n * (sum(y_l²) + sum(y_r²)) - 1/n * (sum(y_l)² / nl + sum(y_r)² / nr)
401          //    = 1/n * sum(y²) - 1/n * (sum(y_l)² / nl + sum(y_r)² / nr)
402          //      -------------
403          //       not changed by split (and the same for total variance without partitioning)
404          //
405          //   therefore we need to find the maximum value (sum(y_l)² / nl + sum(y_r)² / nr) (ignoring the factor 1/n)
406          //   and this value must be larger than 1/n * sum(y)² to be an improvement over no split
407
408          double curQuality = sl * sl / nl + sr * sr / nr;
409
410          if (curQuality > bestImprovement) {
411            bestThreshold = (x[i] + x[i + 1]) / 2.0;
412            bestImprovement = curQuality;
413          }
414        }
415      }
416
417      // if all elements where the same then no split can be found
418    }
419
420
421    private void UpdateVariableRelevance(string bestVar, double sumY, double bestImprovement, int rows) {
422      if (string.IsNullOrEmpty(bestVar)) return;
423      // update variable relevance
424      double baseLine = 1.0 / rows * sumY * sumY; // if best improvement is equal to baseline then the split had no effect
425
426      double delta = (bestImprovement - baseLine);
427      double v;
428      if (!sumImprovements.TryGetValue(bestVar, out v)) {
429        sumImprovements[bestVar] = delta;
430      }
431      sumImprovements[bestVar] = v + delta;
432    }
433
434    public IEnumerable<KeyValuePair<string, double>> GetVariableRelevance() {
435      // values are scaled: the most important variable has relevance = 100
436      double scaling = 100 / sumImprovements.Max(t => t.Value);
437      return
438        sumImprovements
439        .Select(t => new KeyValuePair<string, double>(t.Key, t.Value * scaling))
440        .OrderByDescending(t => t.Value);
441    }
442
443
444    // insert a new parition split (find insertion point and start at first element of the queue)
445    // elements are removed from the queue at the last position
446    // O(n), splits could be organized as a heap to improve runtime (see alglib tsort)
447    private void InsertSortedQueue(PartitionSplits split) {
448      // find insertion position
449      int i = 0;
450      while (i < queue.Count && queue[i].SplittingImprovement < split.SplittingImprovement) { i++; }
451
452      queue.Insert(i, split);
453    }
454  }
455}
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