source: branches/GBT/HeuristicLab.Algorithms.DataAnalysis/3.4/GradientBoostedTrees/RegressionTreeBuilder.cs @ 12372

Last change on this file since 12372 was 12372, checked in by gkronber, 5 years ago

#2261: implemented prototype view for gradient boosted trees

File size: 14.3 KB
Line 
1using System;
2using System.Collections.Generic;
3using System.Diagnostics;
4using System.Diagnostics.Contracts;
5using System.Linq;
6using HeuristicLab.Common;
7using HeuristicLab.Core;
8using HeuristicLab.Problems.DataAnalysis;
9
10namespace GradientBoostedTrees {
11  public class RegressionTreeBuilder {
12    private readonly IRandom random;
13    private readonly IRegressionProblemData problemData;
14
15    private readonly int nCols;
16    private readonly double[][] x; // all training data (original order from problemData)
17    private double[] y; // training labels (original order from problemData)
18
19    private Dictionary<string, double> sumImprovements; // for variable relevance calculation
20
21    private readonly string[] allowedVariables; // all variables in shuffled order
22    private Dictionary<string, int> varName2Index; // maps the variable names to column indexes
23    private int effectiveVars; // number of variables that are used from allowedVariables
24
25    private int effectiveRows; // number of rows that are used from
26    private readonly int[][] sortedIdxAll;
27    private readonly int[][] sortedIdx; // random selection from sortedIdxAll (for r < 1.0)
28
29
30
31    // helper arrays which are allocated to maximal necessary size only once in the ctor
32    private readonly int[] internalIdx, which, leftTmp, rightTmp;
33    private readonly double[] outx;
34    private readonly int[] outSortedIdx;
35
36    private RegressionTreeModel.TreeNode[] tree; // tree is represented as a flat array of nodes
37    private int curTreeNodeIdx; // the index where the next tree node is stored
38
39    private readonly IList<RegressionTreeModel.TreeNode> nodeQueue; //TODO
40
41    // prepare and allocate buffer variables in ctor
42    public RegressionTreeBuilder(IRegressionProblemData problemData, IRandom random) {
43      this.problemData = problemData;
44      this.random = random;
45
46      var rows = problemData.TrainingIndices.Count();
47
48      this.nCols = problemData.AllowedInputVariables.Count();
49
50      allowedVariables = problemData.AllowedInputVariables.ToArray();
51      varName2Index = new Dictionary<string, int>(allowedVariables.Length);
52      for (int i = 0; i < allowedVariables.Length; i++) varName2Index.Add(allowedVariables[i], i);
53
54      sortedIdxAll = new int[nCols][];
55      sortedIdx = new int[nCols][];
56      sumImprovements = new Dictionary<string, double>();
57      internalIdx = new int[rows];
58      which = new int[rows];
59      leftTmp = new int[rows];
60      rightTmp = new int[rows];
61      outx = new double[rows];
62      outSortedIdx = new int[rows];
63      nodeQueue = new List<RegressionTreeModel.TreeNode>();
64
65      x = new double[nCols][];
66      y = problemData.Dataset.GetDoubleValues(problemData.TargetVariable, problemData.TrainingIndices).ToArray();
67
68
69      int col = 0;
70      foreach (var inputVariable in problemData.AllowedInputVariables) {
71        x[col] = problemData.Dataset.GetDoubleValues(inputVariable, problemData.TrainingIndices).ToArray();
72        sortedIdxAll[col] = Enumerable.Range(0, rows).OrderBy(r => x[col][r]).ToArray();
73        sortedIdx[col] = new int[rows];
74        col++;
75      }
76    }
77
78    // r and m work in the same way as for alglib random forest
79    // r is fraction of rows to use for training
80    // m is fraction of variables to use for training
81    public IRegressionModel CreateRegressionTree(int maxDepth, double r = 0.5, double m = 0.5) {
82      // subtract mean of y first
83      var yAvg = y.Average();
84      for (int i = 0; i < y.Length; i++) y[i] -= yAvg;
85
86      var seLoss = new SquaredErrorLoss();
87      var zeros = Enumerable.Repeat(0.0, y.Length);
88      var ones = Enumerable.Repeat(1.0, y.Length);
89
90      var model = CreateRegressionTreeForGradientBoosting(y, maxDepth, problemData.TrainingIndices.ToArray(), seLoss.GetLineSearchFunc(y, zeros, ones), r, m);
91      return new GradientBoostedTreesModel(new[] { new ConstantRegressionModel(yAvg), model }, new[] { 1.0, 1.0 });
92    }
93
94    // specific interface that allows to specify the target labels and the training rows which is necessary when this functionality is called by the gradient boosting routine
95    public IRegressionModel CreateRegressionTreeForGradientBoosting(double[] y, int maxDepth, int[] idx, LineSearchFunc lineSearch, double r = 0.5, double m = 0.5) {
96      Contract.Assert(maxDepth > 0);
97      Contract.Assert(r > 0);
98      Contract.Assert(r <= 1.0);
99      Contract.Assert(y.Count() == this.y.Length);
100      Contract.Assert(m > 0);
101      Contract.Assert(m <= 1.0);
102
103      this.y = y; // y is changed in gradient boosting
104
105      // shuffle row idx
106      HeuristicLab.Random.ListExtensions.ShuffleInPlace(idx, random);
107
108      int nRows = idx.Count();
109
110      // shuffle variable idx
111      HeuristicLab.Random.ListExtensions.ShuffleInPlace(allowedVariables, random);
112
113      effectiveRows = (int)Math.Ceiling(nRows * r);
114      effectiveVars = (int)Math.Ceiling(nCols * m);
115
116      Array.Clear(which, 0, which.Length);
117
118      // mark selected rows
119      for (int row = 0; row < effectiveRows; row++) {
120        which[idx[row]] = 1;
121        internalIdx[row] = idx[row];
122      }
123
124      for (int col = 0; col < nCols; col++) {
125        int i = 0;
126        for (int row = 0; row < nRows; row++) {
127          if (which[sortedIdxAll[col][row]] > 0) {
128            Trace.Assert(i < effectiveRows);
129            sortedIdx[col][i] = sortedIdxAll[col][row];
130            i++;
131          }
132        }
133      }
134
135      // prepare array for the tree nodes (a tree of maxDepth=1 has 1 node, a tree of maxDepth=d has 2^d - 1 nodes)     
136      int numNodes = (int)Math.Pow(2, maxDepth) - 1;
137      //this.tree = new RegressionTreeModel.TreeNode[numNodes];
138      this.tree = Enumerable.Range(0, numNodes).Select(_=>new RegressionTreeModel.TreeNode()).ToArray();
139      this.curTreeNodeIdx = 0;
140
141      // start and end idx are inclusive
142      CreateRegressionTreeForIdx(maxDepth, 0, effectiveRows - 1, lineSearch);
143      return new RegressionTreeModel(tree);
144    }
145
146    // startIdx and endIdx are inclusive
147    private void CreateRegressionTreeForIdx(int maxDepth, int startIdx, int endIdx, LineSearchFunc lineSearch) {
148      Contract.Assert(endIdx - startIdx >= 0);
149      Contract.Assert(startIdx >= 0);
150      Contract.Assert(endIdx < internalIdx.Length);
151
152      // TODO: stop when y is constant
153      // TODO: use priority queue of nodes to be expanded (sorted by improvement) instead of the recursion to maximum depth
154      if (maxDepth <= 1 || endIdx - startIdx == 0) {
155        // max depth reached or only one element   
156        tree[curTreeNodeIdx].varName = RegressionTreeModel.TreeNode.NO_VARIABLE;
157        tree[curTreeNodeIdx].val = lineSearch(internalIdx, startIdx, endIdx);
158        curTreeNodeIdx++;
159      } else {
160        int i, j;
161        double threshold;
162        string bestVariableName;
163        FindBestVariableAndThreshold(startIdx, endIdx, out threshold, out bestVariableName);
164
165        // if bestVariableName is NO_VARIABLE then no split was possible anymore
166        if (bestVariableName == RegressionTreeModel.TreeNode.NO_VARIABLE) {
167          // max depth reached or only one element   
168          tree[curTreeNodeIdx].varName = RegressionTreeModel.TreeNode.NO_VARIABLE;
169          tree[curTreeNodeIdx].val = lineSearch(internalIdx, startIdx, endIdx);
170          curTreeNodeIdx++;
171        } else {
172
173
174          int bestVarIdx = varName2Index[bestVariableName];
175          // split - two pass
176
177          // store which index goes where
178          for (int k = startIdx; k <= endIdx; k++) {
179            if (x[bestVarIdx][internalIdx[k]] <= threshold)
180              which[internalIdx[k]] = -1; // left partition
181            else
182              which[internalIdx[k]] = 1; // right partition
183          }
184
185          // partition sortedIdx for each variable
186          for (int col = 0; col < nCols; col++) {
187            i = 0;
188            j = 0;
189            int k;
190            for (k = startIdx; k <= endIdx; k++) {
191              Debug.Assert(Math.Abs(which[sortedIdx[col][k]]) == 1);
192
193              if (which[sortedIdx[col][k]] < 0) {
194                leftTmp[i++] = sortedIdx[col][k];
195              } else {
196                rightTmp[j++] = sortedIdx[col][k];
197              }
198            }
199            Debug.Assert(i > 0); // at least on element in the left partition
200            Debug.Assert(j > 0); // at least one element in the right partition
201            Debug.Assert(i + j == endIdx - startIdx + 1);
202            k = startIdx;
203            for (int l = 0; l < i; l++) sortedIdx[col][k++] = leftTmp[l];
204            for (int l = 0; l < j; l++) sortedIdx[col][k++] = rightTmp[l];
205          }
206
207          // partition row indices
208          i = startIdx;
209          j = endIdx;
210          while (i <= j) {
211            Debug.Assert(Math.Abs(which[internalIdx[i]]) == 1);
212            Debug.Assert(Math.Abs(which[internalIdx[j]]) == 1);
213            if (which[internalIdx[i]] < 0) i++;
214            else if (which[internalIdx[j]] > 0) j--;
215            else {
216              Trace.Assert(which[internalIdx[i]] > 0);
217              Trace.Assert(which[internalIdx[j]] < 0);
218              // swap
219              int tmp = internalIdx[i];
220              internalIdx[i] = internalIdx[j];
221              internalIdx[j] = tmp;
222              i++;
223              j--;
224            }
225          }
226          Debug.Assert(j < i);
227          Debug.Assert(i >= startIdx);
228          Debug.Assert(j <= endIdx);
229
230          var parentIdx = curTreeNodeIdx;
231          tree[parentIdx].varName = bestVariableName;
232          tree[parentIdx].val = threshold;
233          curTreeNodeIdx++;
234
235          // create left subtree
236          tree[parentIdx].leftIdx = curTreeNodeIdx;
237          CreateRegressionTreeForIdx(maxDepth - 1, startIdx, j, lineSearch);
238
239          // create right subtree
240          tree[parentIdx].rightIdx = curTreeNodeIdx;
241          CreateRegressionTreeForIdx(maxDepth - 1, i, endIdx, lineSearch);
242        }
243      }
244    }
245
246    private void FindBestVariableAndThreshold(int startIdx, int endIdx, out double threshold, out string bestVar) {
247      Contract.Assert(startIdx < endIdx + 1); // at least 2 elements
248
249      int rows = endIdx - startIdx + 1;
250      Contract.Assert(rows >= 2);
251
252      double sumY = 0.0;
253      for (int i = startIdx; i <= endIdx; i++) {
254        sumY += y[internalIdx[i]];
255      }
256
257      double bestImprovement = 0.0;
258      double bestThreshold = double.PositiveInfinity;
259      bestVar = string.Empty;
260
261      for (int col = 0; col < effectiveVars; col++) {
262        // sort values for variable to prepare for threshold selection
263        var curVariable = allowedVariables[col];
264        var curVariableIdx = varName2Index[curVariable];
265        for (int i = startIdx; i <= endIdx; i++) {
266          var sortedI = sortedIdx[curVariableIdx][i];
267          outSortedIdx[i - startIdx] = sortedI;
268          outx[i - startIdx] = x[curVariableIdx][sortedI];
269        }
270
271        double curImprovement;
272        double curThreshold;
273        FindBestThreshold(outx, outSortedIdx, rows, y, sumY, out curThreshold, out curImprovement);
274
275        if (curImprovement > bestImprovement) {
276          bestImprovement = curImprovement;
277          bestThreshold = curThreshold;
278          bestVar = allowedVariables[col];
279        }
280      }
281
282      UpdateVariableRelevance(bestVar, sumY, bestImprovement, rows);
283
284      threshold = bestThreshold;
285
286      // Contract.Assert(bestImprovement > 0);
287      // Contract.Assert(bestImprovement < double.PositiveInfinity);
288      // Contract.Assert(bestVar != string.Empty);
289      // Contract.Assert(allowedVariables.Contains(bestVar));
290    }
291
292    // assumption is that the Average(y) = 0
293    private void UpdateVariableRelevance(string bestVar, double sumY, double bestImprovement, int rows) {
294      if (string.IsNullOrEmpty(bestVar)) return;
295      // update variable relevance
296      double err = sumY * sumY / rows;
297      double errAfterSplit = bestImprovement;
298
299      double delta = (errAfterSplit - err); // relative reduction in squared error
300      double v;
301      if (!sumImprovements.TryGetValue(bestVar, out v)) {
302        sumImprovements[bestVar] = delta;
303      }
304      sumImprovements[bestVar] = v + delta;
305    }
306
307    // x [0..N-1] contains rows sorted values in the range from [0..rows-1]
308    // sortedIdx [0..N-1] contains the idx of the values in x in the original dataset in the range from [0..rows-1]
309    // rows specifies the number of valid entries in x and sortedIdx
310    // y [0..N-1] contains the target values in original sorting order
311    // sumY is y.Sum()
312    //
313    // the routine returns the best threshold (x[i] + x[i+1]) / 2 for i = [0 .. rows-2] by calculating the reduction in squared error
314    // additionally the reduction in squared error is returned in bestImprovement
315    // if all elements of x are equal the routing fails to produce a threshold
316    private static void FindBestThreshold(double[] x, int[] sortedIdx, int rows, double[] y, double sumY, out double bestThreshold, out double bestImprovement) {
317      Contract.Assert(rows >= 2);
318
319      double sl = 0.0;
320      double sr = sumY;
321      double nl = 0.0;
322      double nr = rows;
323
324      bestImprovement = 0.0;
325      bestThreshold = double.NegativeInfinity;
326      // for all thresholds
327      // if we have n rows there are n-1 possible splits
328      for (int i = 0; i < rows - 1; i++) {
329        sl += y[sortedIdx[i]];
330        sr -= y[sortedIdx[i]];
331
332        nl++;
333        nr--;
334        Debug.Assert(nl > 0);
335        Debug.Assert(nr > 0);
336
337        if (x[i] < x[i + 1]) { // don't try to split when two elements are equal
338          double curQuality = sl * sl / nl + sr * sr / nr;
339          // curQuality = nl*nr / (nl+nr) * Sqr(sl / nl - sr / nr) // greedy function approximation page 12 eqn (35)
340
341          if (curQuality > bestImprovement) {
342            bestThreshold = (x[i] + x[i + 1]) / 2.0;
343            bestImprovement = curQuality;
344          }
345        }
346      }
347
348      // if all elements where the same then no split can be found
349    }
350
351
352    public IEnumerable<KeyValuePair<string, double>> GetVariableRelevance() {
353      double scaling = 100 / sumImprovements.Max(t => t.Value);
354      return
355        sumImprovements
356        .Select(t => new KeyValuePair<string, double>(t.Key, t.Value * scaling))
357        .OrderByDescending(t => t.Value);
358    }
359  }
360}
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