[GitHub] [incubator-mxnet] haojin2 commented on a change in pull request #14617: PDF operators for the random samplers, and also the Dirichlet

[GitBox <gi...@apache.org>]

haojin2 commented on a change in pull request #14617: PDF operators for the random samplers, and also the Dirichlet
URL: https://github.com/apache/incubator-mxnet/pull/14617#discussion_r280231148
 
 

 ##########
 File path: src/operator/random/pdf_op.h
 ##########
 @@ -0,0 +1,613 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+
+/*!
+ * Copyright (c) 2018 by Contributors
+ * \file pdf_op.h
+ * \brief Operators for computing the pdf of random distributions.
+ */
+#ifndef MXNET_OPERATOR_RANDOM_PDF_OP_H_
+#define MXNET_OPERATOR_RANDOM_PDF_OP_H_
+
+#include <mxnet/operator_util.h>
+#include <vector>
+#include <algorithm>
+#include "../mshadow_op.h"
+#include "../mxnet_op.h"
+#include "../operator_common.h"
+#include "../elemwise_op_common.h"
+#include "../special_functions-inl.h"
+#include "../tensor/broadcast_reduce_op.h"
+
+namespace mxnet {
+namespace op {
+
+template<typename DType>
+MSHADOW_XINLINE static DType ceph_psi(DType val) { return special_functions::cephes::psi(val); }
+template<>
+MSHADOW_XINLINE mshadow::half::half_t ceph_psi(mshadow::half::half_t val) {
+    return special_functions::cephes::psi<float>(val);
+}
+
+template<bool logpdf>
+struct PDF_Uniform {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size,
+                                  DType *out, IType1 *sample, IType2 *lower, IType2 *upper) {
+    const int index(start / sample_size);
+    const DType l(lower[index]), h(upper[index]);
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        // No check whether sample is in the support.
+        out[i] = logpdf ? -DType(log(h-l)) : DType(1.0)/(h-l);
+    }
+  }
+};
+
+template<bool logpdf>
+struct PDF_Uniform_Grad {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req,
+                  DType *out, IType1 *sample, IType2 *lower, IType2 *upper,
+                  DType *grad_out, IType1 *grad_sample, IType2 *grad_lower, IType2 *grad_upper) {
+    const int index(start / sample_size);
+    const DType l(lower[index]), h(upper[index]);
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i]));
+        grad_lower[i]  = scaling/(h-l);
+        grad_upper[i]  = scaling/(l-h);
+        KERNEL_ASSIGN(grad_sample[i], req, 0);
+    }
+  }
+};
+
+template<bool logpdf>
+struct PDF_Normal {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size,
+                                  DType *out, IType1 *sample, IType2 *loc, IType2 *scale) {
+    const int index(start / sample_size);
+    const DType u(loc[index]), s(scale[index]), sq(s*s);
+    const DType normalizer(sqrt(2.0*mxnet_op::PI)*s);
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const DType x(sample[i]);
+        const DType exponent((DType(-0.5)*(x-u)*(x-u))/(sq));
+        out[i] = logpdf ? exponent-log(normalizer) : exp(exponent)/normalizer;
+    }
+  }
+};
+
+template<bool logpdf>
+struct PDF_Normal_Grad {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req,
+                  DType *out, IType1 *sample, IType2 *loc, IType2 *scale,
+                  DType *grad_out, IType1 *grad_sample, IType2 *grad_loc, IType2 *grad_scale) {
+    const int index(start / sample_size);
+    const DType u(loc[index]), s(scale[index]), s_squared(s*s), s_cubed(s_squared*s);
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const DType x(sample[i]);
+        const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i]));
+        grad_loc[i]    = scaling*(x-u)/s_squared;
+        grad_scale[i]  = scaling*((x-u)*(x-u)-s_squared)/s_cubed;
+        KERNEL_ASSIGN(grad_sample[i], req, scaling*(u-x)/s_squared);
+    }
+  }
+};
+
+template<bool logpdf>
+struct PDF_Gamma {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size,
+                                  DType *out, IType1 *sample, IType2 *alpha, IType2 *beta) {
+    const int index(start / sample_size);
+    const DType a(alpha[index]), b(beta[index]), lgamma_a(lgamma(a)), a_log_b(a*log(b));
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const DType x(sample[i]);
+        const DType lpdf(a_log_b+(a-1)*log(x)-b*x-lgamma_a);
+        out[i] = logpdf ? lpdf : DType(exp(lpdf));
+    }
+  }
+};
+
+template<bool logpdf>
+struct PDF_Gamma_Grad {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req,
+                  DType *out, IType1 *sample, IType2 *alpha, IType2 *beta,
+                  DType *grad_out, IType1 *grad_sample, IType2 *grad_alpha, IType2 *grad_beta) {
+    const int index(start / sample_size);
+    const DType a(alpha[index]), b(beta[index]), log_b(log(b)), ceph_psi_a(ceph_psi(a));
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const DType x(sample[i]);
+        const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i]));
+        grad_alpha[i]  = scaling*(log_b+log(x)-ceph_psi_a);
+        grad_beta[i]   = scaling*(a/b-x);
+        KERNEL_ASSIGN(grad_sample[i], req, scaling*((a-1)/x-b));
+    }
+  }
+};
+
+template<bool logpdf>
+struct PDF_Exponential {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size,
+                                  DType *out, IType1 *sample, IType2 *lambda) {
+    const int index(start / sample_size);
+    const DType l(lambda[index]), log_l(log(l));
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const DType x(sample[i]);
+        out[i] = logpdf ? log_l-l*x : l*exp(-l*x);
+    }
+  }
+};
+
+template<bool logpdf>
+struct PDF_Exponential_Grad {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req,
+                  DType *out, IType1 *sample, IType2 *lambda,
+                  DType *grad_out, IType1 *grad_sample, IType2 *grad_lambda) {
+    const int index(start / sample_size);
+    const DType l(lambda[index]);
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const DType x(sample[i]);
+        const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i]));
+        grad_lambda[i] = scaling*(DType(1)/l-x);
+        KERNEL_ASSIGN(grad_sample[i], req, -scaling*l);
+    }
+  }
+};
+
+template<bool logpdf>
+struct PDF_Poisson {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size,
+                                  DType *out, IType1 *sample, IType2 *lambda) {
+    const int index(start / sample_size);
+    const DType l(lambda[index]), log_l(log(l));
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const DType x(sample[i]);
+        const DType lpdf((x*log_l-lgamma(x+1))-l);
+        out[i] = logpdf ? lpdf  : DType(exp(lpdf));
+    }
+  }
+};
+
+template<bool logpdf>
+struct PDF_Poisson_Grad {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req,
+                  DType *out, IType1 *sample, IType2 *lambda,
+                  DType *grad_out, IType1 *grad_sample, IType2 *grad_lambda) {
+    const int index(start / sample_size);
+    const DType l(lambda[index]);
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const DType x(sample[i]);
+        const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i]));
+        grad_lambda[i] = scaling*(x/l-DType(1));
+        KERNEL_ASSIGN(grad_sample[i], req, 0);
+    }
+  }
+};
+
+
+template<bool logpdf>
+struct PDF_NegativeBinomial {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size,
+                                  DType *out, IType1 *sample, IType2 *limit, IType2 *prob) {
+    const int index(start / sample_size);
+    const DType l(limit[index]), p(prob[index]), lgamma_l(lgamma(l));
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const DType x(sample[i]);
+        const DType lpdf((lgamma(x+l)-lgamma(x+1)-lgamma_l)+l*log(p)+x*log(1-p));
+        out[i] = logpdf ? lpdf : DType(exp(lpdf));
+    }
+  }
+
+  template<typename DType>
+  MSHADOW_XINLINE static DType LPDF(DType l, DType p, DType x) {
+    // Note that "p" is the failure and not the success probability.
+    return (lgamma(x+l)-lgamma(x+1)-lgamma(l))+l*log(p)+x*log(1-p);
+  }
+};
+
+template<bool logpdf>
+struct PDF_NegativeBinomial_Grad {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req,
+                  DType *out, IType1 *sample, IType2 *limit, IType2 *prob,
+                  DType *grad_out, IType1 *grad_sample, IType2 *grad_limit, IType2 *grad_prob) {
+    const int index(start / sample_size);
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        DType grad_l(0), grad_p(0);
+        LPDF_GRAD(DType(limit[index]), DType(prob[index]),
+                  DType(sample[i]), out[i],
+                  grad_out[i], &grad_l, &grad_p);
+        grad_limit[i]  = grad_l;
+        grad_prob[i]   = grad_p;
+        KERNEL_ASSIGN(grad_sample[i], req, 0);
+    }
+  }
+
+  template<typename DType>
+  MSHADOW_XINLINE static void LPDF_GRAD(DType l, DType p, DType x, DType o, DType grad_o,
+                                        DType* grad_l, DType* grad_p) {
+    const DType scaling(grad_o*(logpdf ? DType(1) : o));
+    *grad_l = scaling*((ceph_psi(x+l)-ceph_psi(l))+log(p));
+    *grad_p = scaling*(l/p-x/(1-p));
+  }
+};
+
+template<bool logpdf>
+struct PDF_GeneralizedNegativeBinomial {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size,
+                                  DType *out, IType1 *sample, IType2 *mu, IType2 *alpha) {
+    const int index(start / sample_size);
+
+    // Reparameterize with limit = 1/alpha, prob = 1/(mu*alpha+1)
+    const DType limit(1.0/alpha[index]), prob(1.0/(mu[index]*alpha[index]+1.0));
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const DType lpdf(PDF_NegativeBinomial<logpdf>::LPDF(limit, prob, DType(sample[i])));
+        out[i] = logpdf ? lpdf : DType(exp(lpdf));
+    }
+  }
+};
+
+template<bool logpdf>
+struct PDF_GeneralizedNegativeBinomial_Grad {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req,
+                  DType *out, IType1 *sample, IType2 *mu, IType2 *alpha,
+                  DType *grad_out, IType1 *grad_sample, IType2 *grad_mu, IType2 *grad_alpha) {
+    const int index(start / sample_size);
+    const DType fmu(mu[index]), falpha(alpha[index]), den(fmu*falpha+1.0);
+
+    // Reparameterize with limit = 1/alpha, prob = 1/(mu*alpha+1)
+    const DType limit(1.0/falpha), prob(1.0/(fmu*falpha+1.0));
+
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        // Grad returned as d_limit, d_prob
+        DType grad_l(0), grad_p(0);
+        PDF_NegativeBinomial_Grad<logpdf>::LPDF_GRAD(limit, prob,
+            DType(sample[i]), out[i],
+            grad_out[i], &grad_l, &grad_p);
+        grad_mu[i]     = -grad_p*falpha/(den*den);
+        grad_alpha[i]  = -grad_l/(falpha*falpha)-grad_p*fmu/(den*den);
+        KERNEL_ASSIGN(grad_sample[i], req, 0);
+    }
+  }
+};
+
+template<bool logpdf>
+struct PDF_Dirichlet {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size, int k,
+                                  DType *out, IType1 *sample, IType2 *alpha) {
+    const int index(start / sample_size);
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        const IType1 *cur_sample = sample+i*k;
+        const IType2 *cur_alpha  = alpha+index*k;
+        DType sum_alpha(0), sum_lgamma(0), sum_sample(0);
+        for ( int j = 0; j < k; ++j ) {
+          sum_alpha  += cur_alpha[j];
+          sum_lgamma += lgamma(cur_alpha[j]);
+          sum_sample += (cur_alpha[j]-1)*log(cur_sample[j]);
+        }
+        DType lpdf(sum_sample+(lgamma(sum_alpha)-sum_lgamma));
+        out[i] = logpdf ? lpdf : DType(exp(lpdf));
+    }
+  }
+};
+
+
+template<bool logpdf>
+struct PDF_Dirichlet_Grad {
+  template<typename DType, typename IType1, typename IType2>
+  MSHADOW_XINLINE static void Map(int start, int length, int sample_size,
+                  OpReqType req, int k,
+                  DType *out, IType1 *sample, IType2 *alpha,
+                  DType *grad_out, IType1 *grad_sample, IType2 *grad_alpha) {
+    const int index(start / sample_size);
+    const int end = start + length;
+    for (int i = start; i < end; ++i) {
+        // Digamma function
+        const IType1 *cur_sample = sample+i*k;
+        const IType2 *cur_alpha  = alpha+index*k;
+        const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i]));
+        DType sum_alpha(0);
+        for ( int j = 0; j < k; ++j ) {
 
 Review comment:
   Nit: Don't need the extra spaces within the parentheses
   ```c++
   for (int j = 0; j < k; ++j) {
   ```
   Same for several other places.

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