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fix: заменён алгоритм моделирования полиномов и исправлен прогноз (#122)
This commit is contained in:
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parent
23edbdf371
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f17644dd15
@ -23,6 +23,7 @@ disable=
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fixme,
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missing-docstring,
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too-many-public-methods,
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too-many-locals,
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too-few-public-methods,
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too-many-arguments,
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broad-except
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705
poetry.lock
generated
705
poetry.lock
generated
@ -1,4 +1,4 @@
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# This file is automatically @generated by Poetry 1.6.1 and should not be changed by hand.
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# This file is automatically @generated by Poetry 1.7.1 and should not be changed by hand.
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[[package]]
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name = "altgraph"
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@ -137,119 +137,120 @@ tests = ["pytest", "pytest-cov", "pytest-xdist"]
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[[package]]
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name = "dill"
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version = "0.3.7"
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version = "0.3.8"
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description = "serialize all of Python"
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optional = false
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python-versions = ">=3.7"
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python-versions = ">=3.8"
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files = [
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[package.extras]
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graph = ["objgraph (>=1.7.2)"]
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profile = ["gprof2dot (>=2022.7.29)"]
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[[package]]
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name = "distlib"
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version = "0.3.7"
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version = "0.3.8"
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description = "Distribution utilities"
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optional = false
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python-versions = "*"
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files = [
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{file = "distlib-0.3.7-py2.py3-none-any.whl", hash = "sha256:2e24928bc811348f0feb63014e97aaae3037f2cf48712d51ae61df7fd6075057"},
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name = "filelock"
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version = "3.12.4"
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version = "3.13.1"
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description = "A platform independent file lock."
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optional = false
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python-versions = ">=3.8"
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files = [
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[package.extras]
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docs = ["furo (>=2023.7.26)", "sphinx (>=7.1.2)", "sphinx-autodoc-typehints (>=1.24)"]
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testing = ["covdefaults (>=2.3)", "coverage (>=7.3)", "diff-cover (>=7.7)", "pytest (>=7.4)", "pytest-cov (>=4.1)", "pytest-mock (>=3.11.1)", "pytest-timeout (>=2.1)"]
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typing = ["typing-extensions (>=4.7.1)"]
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docs = ["furo (>=2023.9.10)", "sphinx (>=7.2.6)", "sphinx-autodoc-typehints (>=1.24)"]
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testing = ["covdefaults (>=2.3)", "coverage (>=7.3.2)", "diff-cover (>=8)", "pytest (>=7.4.3)", "pytest-cov (>=4.1)", "pytest-mock (>=3.12)", "pytest-timeout (>=2.2)"]
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typing = ["typing-extensions (>=4.8)"]
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[[package]]
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name = "fonttools"
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version = "4.43.1"
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version = "4.49.0"
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description = "Tools to manipulate font files"
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optional = false
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python-versions = ">=3.8"
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files = [
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]
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||||
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||||
[[package]]
|
||||
@ -483,58 +493,58 @@ altgraph = ">=0.17"
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||||
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||||
[[package]]
|
||||
name = "matplotlib"
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||||
version = "3.7.3"
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||||
version = "3.7.4"
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||||
description = "Python plotting package"
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||||
optional = false
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[[package]]
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setuptools = ">=42.0.0"
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[package.extras]
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hook-testing = ["execnet (>=1.5.0)", "psutil", "pytest (>=2.7.3)"]
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[[package]]
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name = "pyinstaller-hooks-contrib"
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version = "2023.10"
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version = "2024.1"
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description = "Community maintained hooks for PyInstaller"
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optional = false
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setuptools = ">=42.0.0"
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|
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[[package]]
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name = "pylint"
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@ -945,13 +960,13 @@ six = ">=1.5"
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|
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[[package]]
|
||||
name = "pytz"
|
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version = "2023.3.post1"
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[[package]]
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|
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[[package]]
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||||
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|
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python-versions = ">=3.8"
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||||
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||||
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||||
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||||
|
||||
[package.extras]
|
||||
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||||
|
||||
[[package]]
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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|
||||
|
||||
[[package]]
|
||||
name = "setuptools-scm"
|
||||
version = "8.0.4"
|
||||
description = "the blessed package to manage your versions by scm tags"
|
||||
optional = false
|
||||
python-versions = ">=3.8"
|
||||
files = [
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||||
|
||||
[package.dependencies]
|
||||
packaging = ">=20"
|
||||
setuptools = "*"
|
||||
tomli = {version = ">=1", markers = "python_version < \"3.11\""}
|
||||
typing-extensions = "*"
|
||||
|
||||
[package.extras]
|
||||
docs = ["entangled-cli[rich]", "mkdocs", "mkdocs-entangled-plugin", "mkdocs-material", "mkdocstrings[python]", "pygments"]
|
||||
rich = ["rich"]
|
||||
test = ["build", "pytest", "rich", "wheel"]
|
||||
|
||||
[[package]]
|
||||
name = "shiboken2"
|
||||
version = "5.15.2.1"
|
||||
@ -1102,6 +1181,17 @@ files = [
|
||||
[package.dependencies]
|
||||
mpmath = ">=0.19"
|
||||
|
||||
[[package]]
|
||||
name = "threadpoolctl"
|
||||
version = "3.3.0"
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||||
description = "threadpoolctl"
|
||||
optional = false
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||||
python-versions = ">=3.8"
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]
|
||||
|
||||
[[package]]
|
||||
name = "tomli"
|
||||
version = "2.0.1"
|
||||
@ -1115,52 +1205,52 @@ files = [
|
||||
|
||||
[[package]]
|
||||
name = "tomlkit"
|
||||
version = "0.12.1"
|
||||
version = "0.12.3"
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||||
description = "Style preserving TOML library"
|
||||
optional = false
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||||
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name = "typing-extensions"
|
||||
version = "4.8.0"
|
||||
version = "4.9.0"
|
||||
description = "Backported and Experimental Type Hints for Python 3.8+"
|
||||
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|
||||
[[package]]
|
||||
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|
||||
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|
||||
version = "2024.1"
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
[package.extras]
|
||||
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|
||||
@ -1168,86 +1258,81 @@ test = ["covdefaults (>=2.3)", "coverage (>=7.2.7)", "coverage-enable-subprocess
|
||||
|
||||
[[package]]
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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{file = "wrapt-1.16.0-cp38-cp38-win_amd64.whl", hash = "sha256:490b0ee15c1a55be9c1bd8609b8cecd60e325f0575fc98f50058eae366e01f41"},
|
||||
{file = "wrapt-1.16.0-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:9b201ae332c3637a42f02d1045e1d0cccfdc41f1f2f801dafbaa7e9b4797bfc2"},
|
||||
{file = "wrapt-1.16.0-cp39-cp39-macosx_11_0_arm64.whl", hash = "sha256:2076fad65c6736184e77d7d4729b63a6d1ae0b70da4868adeec40989858eb3fb"},
|
||||
{file = "wrapt-1.16.0-cp39-cp39-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:c5cd603b575ebceca7da5a3a251e69561bec509e0b46e4993e1cac402b7247b8"},
|
||||
{file = "wrapt-1.16.0-cp39-cp39-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:b47cfad9e9bbbed2339081f4e346c93ecd7ab504299403320bf85f7f85c7d46c"},
|
||||
{file = "wrapt-1.16.0-cp39-cp39-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:f8212564d49c50eb4565e502814f694e240c55551a5f1bc841d4fcaabb0a9b8a"},
|
||||
{file = "wrapt-1.16.0-cp39-cp39-musllinux_1_1_aarch64.whl", hash = "sha256:5f15814a33e42b04e3de432e573aa557f9f0f56458745c2074952f564c50e664"},
|
||||
{file = "wrapt-1.16.0-cp39-cp39-musllinux_1_1_i686.whl", hash = "sha256:db2e408d983b0e61e238cf579c09ef7020560441906ca990fe8412153e3b291f"},
|
||||
{file = "wrapt-1.16.0-cp39-cp39-musllinux_1_1_x86_64.whl", hash = "sha256:edfad1d29c73f9b863ebe7082ae9321374ccb10879eeabc84ba3b69f2579d537"},
|
||||
{file = "wrapt-1.16.0-cp39-cp39-win32.whl", hash = "sha256:ed867c42c268f876097248e05b6117a65bcd1e63b779e916fe2e33cd6fd0d3c3"},
|
||||
{file = "wrapt-1.16.0-cp39-cp39-win_amd64.whl", hash = "sha256:eb1b046be06b0fce7249f1d025cd359b4b80fc1c3e24ad9eca33e0dcdb2e4a35"},
|
||||
{file = "wrapt-1.16.0-py3-none-any.whl", hash = "sha256:6906c4100a8fcbf2fa735f6059214bb13b97f75b1a61777fcf6432121ef12ef1"},
|
||||
{file = "wrapt-1.16.0.tar.gz", hash = "sha256:5f370f952971e7d17c7d1ead40e49f32345a7f7a5373571ef44d800d06b1899d"},
|
||||
]
|
||||
|
||||
[[package]]
|
||||
@ -1268,4 +1353,4 @@ testing = ["big-O", "jaraco.functools", "jaraco.itertools", "more-itertools", "p
|
||||
[metadata]
|
||||
lock-version = "2.0"
|
||||
python-versions = ">=3.8,<3.9"
|
||||
content-hash = "e8ca19934d2ae7c8fbe0238a777e8d7b8882c86d38a700bdd0495b175f1458fe"
|
||||
content-hash = "2b8a026bc059c637b81c6e65b372f97283956248272a0c41af0b6d350eec14e8"
|
||||
|
||||
@ -20,6 +20,7 @@ pylint = { version = "^2", markers = "python_version < '3.9'" }
|
||||
sympy = "^1.12"
|
||||
matplotlib = "^3.7.0"
|
||||
pillow = "9.5"
|
||||
scikit-learn = "1.3.2"
|
||||
|
||||
|
||||
[build-system]
|
||||
|
||||
@ -1,124 +0,0 @@
|
||||
# Copyright (c) 2023 Matthew Rocklin
|
||||
# All rights reserved.
|
||||
# This source code is distributed under the terms of the BSD license,
|
||||
# which allows you to use, modify, and distribute it
|
||||
# as long as you comply with the license terms.
|
||||
|
||||
# In addition, this code has been modified by Maxim Slipenko and
|
||||
# is now also licensed under the GPL-3.0.
|
||||
# See the GPL-3.0 license for details.
|
||||
|
||||
import itertools
|
||||
from numpy import linalg, zeros, ones, hstack, asarray
|
||||
from sympy import symbols, Mul, Add, S
|
||||
|
||||
|
||||
def basisVector(n, i):
|
||||
""" Return an array like [0, 0, ..., 1, ..., 0, 0]
|
||||
|
||||
>>> from statapp._vendor.multipolyfit import basisVector
|
||||
>>> basis_vector(3, 1)
|
||||
array([0, 1, 0])
|
||||
>>> basisVector(5, 4)
|
||||
array([0, 0, 0, 0, 1])
|
||||
"""
|
||||
x = zeros(n, dtype=int)
|
||||
x[i] = 1
|
||||
return x
|
||||
|
||||
|
||||
def asTall(x):
|
||||
""" Turns a row vector into a column vector """
|
||||
return x.reshape(x.shape + (1,))
|
||||
|
||||
|
||||
def multipolyfit(xs, y, deg, full=False, modelOut=False, powersOut=False):
|
||||
# pylint: disable-msg=too-many-locals
|
||||
"""
|
||||
Least squares multivariate polynomial fit
|
||||
|
||||
Fit a polynomial like ``y = a**2 + 3a - 2ab + 4b**2 - 1``
|
||||
with many covariates a, b, c, ...
|
||||
|
||||
Parameters
|
||||
----------
|
||||
|
||||
xs : array_like, shape (M, k)
|
||||
x-coordinates of the k covariates over the M sample points
|
||||
y : array_like, shape(M,)
|
||||
y-coordinates of the sample points.
|
||||
deg : int
|
||||
Degree o fthe fitting polynomial
|
||||
modelOut : bool (defaults to True)
|
||||
If True return a callable function
|
||||
If False return an array of coefficients
|
||||
powersOut : bool (defaults to False)
|
||||
Returns the meaning of each of the coefficients in the form of an
|
||||
iterator that gives the powers over the inputs and 1
|
||||
For example if xs corresponds to the covariates a,b,c then the array
|
||||
[1, 2, 1, 0] corresponds to 1**1 * a**2 * b**1 * c**0
|
||||
|
||||
See Also
|
||||
--------
|
||||
numpy.polyfit
|
||||
|
||||
"""
|
||||
# pylin
|
||||
y = asarray(y).squeeze()
|
||||
# rows = y.shape[0]
|
||||
xs = asarray(xs)
|
||||
numCovariates = xs.shape[1]
|
||||
xs = hstack((ones((xs.shape[0], 1), dtype=xs.dtype) , xs))
|
||||
|
||||
generators = [basisVector(numCovariates + 1, i)
|
||||
for i in range(numCovariates+1)]
|
||||
|
||||
# All combinations of degrees
|
||||
powers = [sum(x) for x in itertools.combinations_with_replacement(generators, deg)]
|
||||
|
||||
# Raise data to specified degree pattern, stack in order
|
||||
a = hstack(asarray([asTall((xs ** p).prod(1)) for p in powers]))
|
||||
|
||||
result = linalg.lstsq(a, y, rcond=None)
|
||||
beta = result[0]
|
||||
|
||||
if modelOut:
|
||||
return mkModel(beta, powers)
|
||||
|
||||
if powersOut:
|
||||
return beta, powers
|
||||
|
||||
if full:
|
||||
return result, powers, a
|
||||
|
||||
return beta
|
||||
|
||||
|
||||
def mkModel(beta, powers):
|
||||
""" Create a callable python function out of beta/powers from multipolyfit
|
||||
|
||||
This function is callable from within multipolyfit using the model_out flag
|
||||
"""
|
||||
# Create a function that takes in many x values
|
||||
# and returns an approximate y value
|
||||
def model(*args):
|
||||
numCovariates = len(powers[0]) - 1
|
||||
if len(args) != numCovariates:
|
||||
raise ValueError(f"Expected {numCovariates} inputs")
|
||||
xs = asarray((1,) + args)
|
||||
return sum(coeff * (xs**p).prod()
|
||||
for p, coeff in zip(powers, beta))
|
||||
return model
|
||||
|
||||
|
||||
def mkSympyFunction(beta, powers):
|
||||
terms = getTerms(powers)
|
||||
return Add(*[coeff * term for term, coeff in zip(terms, beta)])
|
||||
|
||||
|
||||
def getTerms(powers):
|
||||
numCovariates = len(powers[0])
|
||||
xs = (S.One,) + symbols(f'x1:{numCovariates}')
|
||||
|
||||
terms = [Mul(*[x ** deg for x, deg in zip(xs, power)]) for power in powers]
|
||||
return terms
|
||||
@ -22,7 +22,10 @@ from dataclasses import dataclass
|
||||
import numpy as np
|
||||
import pandas as pd
|
||||
import sympy as sp
|
||||
from statapp._vendor.multipolyfit import multipolyfit, getTerms
|
||||
from sklearn.preprocessing import PolynomialFeatures
|
||||
from sklearn.linear_model import LinearRegression
|
||||
from sklearn.metrics import mean_squared_error
|
||||
|
||||
|
||||
DIRECT_LINK = 0
|
||||
INDIRECT_LINK = 1
|
||||
@ -78,64 +81,99 @@ class RegressionResult:
|
||||
monomials: list
|
||||
|
||||
|
||||
def commonPolynom(inputData, deg) -> RegressionResult:
|
||||
x = inputData[:, 1:]
|
||||
y = inputData[:, 0]
|
||||
result, powers, data = multipolyfit(x, y, deg, full=True)
|
||||
(out, mse, scaledResidualVariance,
|
||||
rSquared, fStatistic) = calculateStats(data, result[0], result[1], y)
|
||||
def linearPolynom(data):
|
||||
y = data[:, 0]
|
||||
x = data[:, 1:]
|
||||
|
||||
polyFeatures = PolynomialFeatures(degree=1, include_bias=False)
|
||||
xPoly = polyFeatures.fit_transform(x)
|
||||
|
||||
model = LinearRegression(fit_intercept=True)
|
||||
model.fit(xPoly, y)
|
||||
|
||||
params = np.hstack([model.intercept_, model.coef_])
|
||||
|
||||
predictions = model.predict(xPoly)
|
||||
residuals = y - predictions
|
||||
mse = mean_squared_error(y, predictions)
|
||||
|
||||
rSquared = model.score(xPoly, y)
|
||||
|
||||
n = xPoly.shape[0]
|
||||
k = xPoly.shape[1] + 1
|
||||
|
||||
fStatistic = (rSquared / (k - 1)) / ((1 - rSquared) / (n - k))
|
||||
|
||||
xWithIntercept = np.hstack([np.ones((n, 1)), xPoly])
|
||||
varB = mse * np.linalg.inv(xWithIntercept.T @ xWithIntercept).diagonal()
|
||||
seB = np.sqrt(varB)
|
||||
|
||||
tStats = params / seB
|
||||
|
||||
monomials = ['c'] + ['x' + str(i) for i in range(1, x.shape[1] + 1)]
|
||||
|
||||
residualVariance = np.var(residuals, ddof=k)
|
||||
scaledResidualVariance = residualVariance / (n - k)
|
||||
|
||||
paramsAndTStats = np.vstack((params, tStats)).T
|
||||
|
||||
return RegressionResult(
|
||||
out.to_numpy(),
|
||||
np.float64(mse),
|
||||
np.float64(scaledResidualVariance),
|
||||
np.float64(rSquared),
|
||||
np.float64(fStatistic),
|
||||
['c' if str(x) == '1' else str(x) for x in getTerms(powers)]
|
||||
paramsAndTStats,
|
||||
residualVariance,
|
||||
scaledResidualVariance,
|
||||
rSquared,
|
||||
fStatistic,
|
||||
monomials
|
||||
)
|
||||
|
||||
|
||||
def linearPolynom(inputData) -> RegressionResult:
|
||||
return commonPolynom(inputData, 1)
|
||||
def squaredPolynom(data):
|
||||
y = data[:, 0]
|
||||
x = data[:, 1:]
|
||||
|
||||
polyFeatures = PolynomialFeatures(degree=2, include_bias=False)
|
||||
xPoly = polyFeatures.fit_transform(x)
|
||||
|
||||
def squaredPolynom(inputData) -> RegressionResult:
|
||||
return commonPolynom(inputData, 2)
|
||||
model = LinearRegression(fit_intercept=True)
|
||||
model.fit(xPoly, y)
|
||||
|
||||
params = np.hstack([model.intercept_, model.coef_])
|
||||
|
||||
def calculateStats(data, params, residues, y):
|
||||
# pylint: disable-msg=too-many-locals
|
||||
predictions = model.predict(xPoly)
|
||||
residuals = y - predictions
|
||||
mse = mean_squared_error(y, predictions)
|
||||
|
||||
k = len(params) # Количество оцениваемых параметров (коэффициентов)
|
||||
n = len(data) # Количество наблюдений
|
||||
rSquared = model.score(xPoly, y)
|
||||
|
||||
# Степень свободы (degrees of freedom) для остатков
|
||||
dof = n - k # Количество наблюдений минус количество оцениваемых параметров
|
||||
# Остаточная дисперсия (Mean Squared Error, MSE)
|
||||
mse = residues / dof
|
||||
# Среднее значение остатков
|
||||
meanResiduals = np.sum(residues) / dof
|
||||
# Масштабированная остаточная дисперсия
|
||||
scaledResidualVariance = residues / meanResiduals ** 2
|
||||
# Ковариационная матрица коэффициентов
|
||||
cov = mse * np.diagonal(np.linalg.inv(data.T @ data))
|
||||
# Стандартные ошибки коэффициентов
|
||||
se = np.sqrt(cov)
|
||||
# T-статистики для каждого коэффициента регрессии
|
||||
tStatistics = params / se
|
||||
n = xPoly.shape[0]
|
||||
k = xPoly.shape[1] + 1
|
||||
|
||||
# R-squared (коэффициент множественной детерминации)
|
||||
sst = np.sum((y - np.mean(y)) ** 2) # Сумма квадратов отклонений
|
||||
rSquared = 1 - (mse[0] / sst)
|
||||
|
||||
# F-statistic (статистика Фишера)
|
||||
fStatistic = (rSquared / (k - 1)) / ((1 - rSquared) / (n - k))
|
||||
|
||||
out = pd.DataFrame()
|
||||
out[0] = params
|
||||
out[1] = tStatistics
|
||||
xWithIntercept = np.hstack([np.ones((n, 1)), xPoly])
|
||||
varB = mse * np.linalg.pinv(xWithIntercept.T @ xWithIntercept).diagonal()
|
||||
seB = np.sqrt(np.maximum(varB, 0))
|
||||
|
||||
return out, mse[0], scaledResidualVariance, rSquared, fStatistic
|
||||
tStats = params / seB
|
||||
|
||||
monomials = ['c'] + list(
|
||||
polyFeatures.get_feature_names_out(['x' + str(i) for i in range(1, x.shape[1] + 1)])
|
||||
)
|
||||
monomials = [monomial.replace(' ', '*') for monomial in monomials]
|
||||
|
||||
residualVariance = np.var(residuals, ddof=k)
|
||||
scaledResidualVariance = residualVariance / (n - k)
|
||||
|
||||
paramsAndTStats = np.vstack((params, tStats)).T
|
||||
|
||||
return RegressionResult(
|
||||
paramsAndTStats,
|
||||
residualVariance,
|
||||
scaledResidualVariance,
|
||||
rSquared,
|
||||
fStatistic,
|
||||
monomials
|
||||
)
|
||||
|
||||
|
||||
def prediction(inputData, result: RegressionResult):
|
||||
@ -153,8 +191,12 @@ def prediction(inputData, result: RegressionResult):
|
||||
|
||||
results = []
|
||||
|
||||
numVars = inputs.shape[1]
|
||||
symbolsStr = ' '.join([f'x{i}' for i in range(1, numVars + 1)])
|
||||
symbols = sp.symbols(symbolsStr)
|
||||
|
||||
for y, xValues in zip(outputs, inputs):
|
||||
subsDict = dict(zip(expr.free_symbols, xValues))
|
||||
subsDict = dict(zip(symbols, xValues))
|
||||
predictedResult = expr.subs(subsDict)
|
||||
difference = predictedResult - y
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user