source: branches/HeuristicLab.RegressionSolutionGradientView/HeuristicLab.Algorithms.DataAnalysis/3.4/GradientBoostedTrees/RegressionTreeBuilder.cs @ 13994

Last change on this file since 13994 was 13994, checked in by bburlacu, 3 years ago

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