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Improve numerical stability of normal quantile gradients #3139

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Improve numerical stability of normal quantile gradients #3139

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1e105c3
Improve numerical stability of normal quantile gradients
andrjohns Jan 13, 2025
a67a993
[Jenkins] auto-formatting by clang-format version 10.0.0-4ubuntu1
stan-buildbot Jan 13, 2025
b713e58
Update vectorisation
andrjohns Jan 13, 2025
d7edcbd
[Jenkins] auto-formatting by clang-format version 10.0.0-4ubuntu1
stan-buildbot Jan 13, 2025
4f53279
Fix opencl headers
andrjohns Jan 14, 2025
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18 changes: 12 additions & 6 deletions stan/math/rev/fun/inv_Phi.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -3,8 +3,10 @@

#include <stan/math/rev/meta.hpp>
#include <stan/math/rev/core.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/inv_Phi.hpp>
#include <stan/math/prim/prob/std_normal_lpdf.hpp>
#include <stan/math/prim/functor/apply_scalar_binary.hpp>
#include <cmath>

namespace stan {
Expand All @@ -19,8 +21,9 @@ namespace math {
* @return The unit normal inverse cdf evaluated at p
*/
inline var inv_Phi(const var& p) {
return make_callback_var(inv_Phi(p.val()), [p](auto& vi) mutable {
p.adj() += vi.adj() * SQRT_TWO_PI / std::exp(-0.5 * vi.val() * vi.val());
double val = inv_Phi(p.val());
return make_callback_var(val, [p, val](auto& vi) mutable {
p.adj() += vi.adj() * exp(-std_normal_lpdf(val));
});
}

Expand All @@ -33,9 +36,12 @@ inline var inv_Phi(const var& p) {
*/
template <typename T, require_var_matrix_t<T>* = nullptr>
inline auto inv_Phi(const T& p) {
return make_callback_var(inv_Phi(p.val()), [p](auto& vi) mutable {
p.adj().array() += vi.adj().array() * SQRT_TWO_PI
/ (-0.5 * vi.val().array().square()).exp();
const auto& arena_rtn = to_arena(inv_Phi(p.val()));
return make_callback_var(arena_rtn, [p, arena_rtn](auto& vi) mutable {
p.adj() += apply_scalar_binary(
vi.adj(), arena_rtn.val(), [](const double adj, const double rtn_val) {
return adj * exp(-std_normal_lpdf(rtn_val));
});
});
}

Expand Down
22 changes: 10 additions & 12 deletions stan/math/rev/prob/std_normal_log_qf.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -3,9 +3,9 @@

#include <stan/math/rev/meta.hpp>
#include <stan/math/rev/core.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/sign.hpp>
#include <stan/math/prim/prob/std_normal_log_qf.hpp>
#include <stan/math/prim/functor/apply_scalar_binary.hpp>
#include <stan/math/prim/fun/elt_multiply.hpp>
#include <cmath>

namespace stan {
Expand All @@ -19,16 +19,14 @@ namespace math {
*/
template <typename T, require_stan_scalar_or_eigen_t<T>* = nullptr>
inline auto std_normal_log_qf(const var_value<T>& log_p) {
return make_callback_var(
std_normal_log_qf(log_p.val()), [log_p](auto& vi) mutable {
auto vi_array = as_array_or_scalar(vi.val());
auto vi_sign = sign(as_array_or_scalar(vi.adj()));

const auto& deriv = as_array_or_scalar(log_p).val()
+ log(as_array_or_scalar(vi.adj()) * vi_sign)
- NEG_LOG_SQRT_TWO_PI + 0.5 * square(vi_array);
as_array_or_scalar(log_p).adj() += vi_sign * exp(deriv);
});
const auto& arena_rtn = to_arena(std_normal_log_qf(log_p.val()));
return make_callback_var(arena_rtn, [log_p, arena_rtn](auto& vi) mutable {
auto deriv = apply_scalar_binary(
log_p.val(), arena_rtn, [](const auto& logp_val, const auto& rtn_val) {
return exp(logp_val - std_normal_lpdf(rtn_val));
});
Comment on lines +24 to +27
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@SteveBronder SteveBronder Jan 15, 2025 •
edited
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Instead of apply_scalar_binary here how do you feel about just doing the std_normal_lpdf on the return val? Since then the rest can use standard vectorization from Eigen.

Suggested change
auto deriv = apply_scalar_binary(
log_p.val(), arena_rtn, [](const auto& logp_val, const auto& rtn_val) {
return exp(logp_val - std_normal_lpdf(rtn_val));
});
if constexpr (is_eigen<decltype(arena_rtn)>::value) {
auto derive = exp(log_p.val() - arena_rtn.unaryExpr([](auto x) {
return std_normal_lpdf(x);}));
log_p.adj() += elt_multiply(vi.adj(), deriv);
} else {
auto derive = exp(log_p.val() - std_normal_lpdf(arena_rtn));
log_p.adj() += vi.adj() * deriv;
}

Same thing for the other change.

log_p.adj() += elt_multiply(vi.adj(), deriv);
});
}

} // namespace math
Expand Down
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