From ae56a721eb63e6e2032e10436a4944d9203aa560 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Wed, 12 Feb 2025 16:23:43 -0300 Subject: More writing --- Makefile | 15 +- figs/fit_basis_abs.pdf | Bin 0 -> 8199 bytes figs/fit_bias-variance_abs.pdf | Bin 0 -> 6184 bytes figs/fit_bias-variance_abs2.pdf | Bin 0 -> 6874 bytes figs/fit_data_abs2.pdf | Bin 0 -> 6408 bytes figs/fit_goodfit_abs.pdf | Bin 0 -> 11791 bytes figs/fit_goodfit_abs2.pdf | Bin 0 -> 7630 bytes figs/fit_gradient_1.pdf | Bin 0 -> 57630 bytes figs/fit_gradient_2.pdf | Bin 0 -> 58063 bytes figs/fit_gradient_3.pdf | Bin 0 -> 59363 bytes figs/fit_gradient_4.pdf | Bin 0 -> 59688 bytes figs/fit_gradient_5.pdf | Bin 0 -> 61905 bytes figs/fit_gradient_6.pdf | Bin 0 -> 75233 bytes figs/fit_overfit_abs.pdf | Bin 0 -> 16236 bytes figs/fit_overfit_abs2.pdf | Bin 0 -> 7996 bytes figs/fit_overparamfit_abs.pdf | Bin 0 -> 18294 bytes figs/fit_overparamfit_abs2.pdf | Bin 0 -> 8642 bytes figs/fit_underfit_abs.pdf | Bin 0 -> 10832 bytes figs/fit_underfit_abs2.pdf | Bin 0 -> 7054 bytes fits.cpp | 15 +- fits.nb | 30664 ++++++++++++++++++-------------------- fits_abs.cpp | 81 + ictp-saifr_colloquium.tex | 350 + test2.dat | 31 + 24 files changed, 15017 insertions(+), 16139 deletions(-) create mode 100644 figs/fit_basis_abs.pdf create mode 100644 figs/fit_bias-variance_abs.pdf create mode 100644 figs/fit_bias-variance_abs2.pdf create mode 100644 figs/fit_data_abs2.pdf create mode 100644 figs/fit_goodfit_abs.pdf create mode 100644 figs/fit_goodfit_abs2.pdf create mode 100644 figs/fit_gradient_1.pdf create mode 100644 figs/fit_gradient_2.pdf create mode 100644 figs/fit_gradient_3.pdf create mode 100644 figs/fit_gradient_4.pdf create mode 100644 figs/fit_gradient_5.pdf create mode 100644 figs/fit_gradient_6.pdf create mode 100644 figs/fit_overfit_abs.pdf create mode 100644 figs/fit_overfit_abs2.pdf create mode 100644 figs/fit_overparamfit_abs.pdf create mode 100644 figs/fit_overparamfit_abs2.pdf create mode 100644 figs/fit_underfit_abs.pdf create mode 100644 figs/fit_underfit_abs2.pdf create mode 100644 fits_abs.cpp create mode 100644 test2.dat diff --git a/Makefile b/Makefile index 1eccaac..d536c18 100644 --- a/Makefile +++ b/Makefile @@ -1,10 +1,15 @@ -all: fits fits_abs many_over +all: fits fits_abs many_over fits_abs_2 + +CC := clang++ -std=c++17 -Wno-mathematical-notation-identifier-extension -O3 -march=native -mtune=native -fopenmp fits: fits.cpp fits.hpp - clang++ -std=c++17 -Wno-mathematical-notation-identifier-extension -O3 -march=native -mtune=native -fopenmp fits.cpp -o fits + $(CC) fits.cpp -o fits many_over: many_over.cpp fits.hpp - clang++ -std=c++17 -Wno-mathematical-notation-identifier-extension -O3 -march=native -mtune=native -fopenmp many_over.cpp -o many_over + $(CC) many_over.cpp -o many_over + +fits_abs: fits_abs.cpp fits.hpp + $(CC) -DFITS_ABS_BASIS fits_abs.cpp -o fits_abs -fits_abs: fits.cpp fits.hpp - clang++ -std=c++17 -Wno-mathematical-notation-identifier-extension -O3 -march=native -mtune=native -fopenmp -DFITS_ABS_BASIS fits.cpp -o fits_abs +fits_abs_2: fits.cpp fits.hpp + $(CC) -DFITS_ABS_BASIS fits.cpp -o fits_abs_2 diff --git a/figs/fit_basis_abs.pdf b/figs/fit_basis_abs.pdf new file mode 100644 index 0000000..4c623ad Binary files /dev/null and b/figs/fit_basis_abs.pdf differ diff --git a/figs/fit_bias-variance_abs.pdf b/figs/fit_bias-variance_abs.pdf new file mode 100644 index 0000000..9fea54c Binary files /dev/null and b/figs/fit_bias-variance_abs.pdf differ diff --git a/figs/fit_bias-variance_abs2.pdf b/figs/fit_bias-variance_abs2.pdf new file mode 100644 index 0000000..4a8742c Binary files /dev/null and b/figs/fit_bias-variance_abs2.pdf differ diff --git a/figs/fit_data_abs2.pdf b/figs/fit_data_abs2.pdf new file mode 100644 index 0000000..400a0bc Binary files /dev/null and b/figs/fit_data_abs2.pdf differ diff --git a/figs/fit_goodfit_abs.pdf b/figs/fit_goodfit_abs.pdf new file mode 100644 index 0000000..76a928f Binary files /dev/null and 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/dev/null and b/figs/fit_gradient_5.pdf differ diff --git a/figs/fit_gradient_6.pdf b/figs/fit_gradient_6.pdf new file mode 100644 index 0000000..fcf3f83 Binary files /dev/null and b/figs/fit_gradient_6.pdf differ diff --git a/figs/fit_overfit_abs.pdf b/figs/fit_overfit_abs.pdf new file mode 100644 index 0000000..5ba03eb Binary files /dev/null and b/figs/fit_overfit_abs.pdf differ diff --git a/figs/fit_overfit_abs2.pdf b/figs/fit_overfit_abs2.pdf new file mode 100644 index 0000000..f80fdbe Binary files /dev/null and b/figs/fit_overfit_abs2.pdf differ diff --git a/figs/fit_overparamfit_abs.pdf b/figs/fit_overparamfit_abs.pdf new file mode 100644 index 0000000..70030bb Binary files /dev/null and b/figs/fit_overparamfit_abs.pdf differ diff --git a/figs/fit_overparamfit_abs2.pdf b/figs/fit_overparamfit_abs2.pdf new file mode 100644 index 0000000..af70cb3 Binary files /dev/null and b/figs/fit_overparamfit_abs2.pdf differ diff --git a/figs/fit_underfit_abs.pdf b/figs/fit_underfit_abs.pdf new file mode 100644 index 0000000..af6cd92 Binary files /dev/null and b/figs/fit_underfit_abs.pdf differ diff --git a/figs/fit_underfit_abs2.pdf b/figs/fit_underfit_abs2.pdf new file mode 100644 index 0000000..eea0bcb Binary files /dev/null and b/figs/fit_underfit_abs2.pdf differ diff --git a/fits.cpp b/fits.cpp index 682886a..d8676bb 100644 --- a/fits.cpp +++ b/fits.cpp @@ -11,9 +11,11 @@ int main(int argc, char* argv[]) { Real iniVar = 0.0; long unsigned maxSteps = 1e12; + bool cosine = false; + int opt; - while ((opt = getopt(argc, argv, "M:s:S:B:i:N:")) != -1) { + while ((opt = getopt(argc, argv, "M:s:S:B:i:N:c:")) != -1) { switch (opt) { case 'N': Nend = (unsigned)atof(optarg); @@ -33,6 +35,9 @@ int main(int argc, char* argv[]) { case 'i': iniVar = atof(optarg); break; + case 'c': + cosine = true; + break; default: exit(1); } @@ -40,7 +45,13 @@ int main(int argc, char* argv[]) { Rng r; - Data data = generateData([](Real x) {return std::sin(2 * M_PI * x);}, M, σ, r); + Data data; + + if (cosine) { + data = generateData([](Real x) {return std::cos(2 * M_PI * x);}, M, σ, r); + } else { + data = generateData([](Real x) {return std::sin(2 * M_PI * x);}, M, σ, r); + } std::cout << std::setprecision(15); diff --git a/fits.nb b/fits.nb index 052ab44..1f4c54e 100644 --- a/fits.nb +++ b/fits.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 154, 7] -NotebookDataLength[ 2831857, 49713] -NotebookOptionsPosition[ 2825203, 49596] -NotebookOutlinePosition[ 2825598, 49612] -CellTagsIndexPosition[ 2825555, 49609] +NotebookDataLength[ 2678771, 48113] +NotebookOptionsPosition[ 2667616, 47933] +NotebookOutlinePosition[ 2668011, 47949] +CellTagsIndexPosition[ 2667968, 47946] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -71,7 +71,7 @@ poly_fits.dat\>\"", "]"}]}], ";"}]], "Input", 3.9481746867275467`*^9}, {3.9481968999131937`*^9, 3.948196900701874*^9}, { 3.9482030689210777`*^9, 3.9482030693756723`*^9}, 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/dev/null +++ b/fits_abs.cpp @@ -0,0 +1,81 @@ +#include +#include + +#include "fits.hpp" + +int main(int argc, char* argv[]) { + unsigned Nend = 1; + unsigned nBatches = 5; + Real σ = 0.2; + Real iniVar = 0.0; + long unsigned maxSteps = 1e12; + + int opt; + + while ((opt = getopt(argc, argv, "s:S:B:i:N:")) != -1) { + switch (opt) { + case 'N': + Nend = (unsigned)atof(optarg); + break; + case 's': + σ = atof(optarg); + break; + case 'S': + maxSteps = (long unsigned)atof(optarg); + break; + case 'B': + nBatches = (unsigned)atof(optarg); + break; + case 'i': + iniVar = atof(optarg); + break; + default: + exit(1); + } + } + + std::string firstline; + std::getline(std::cin, firstline); + std::stringstream ss; + ss << firstline; + + Data data; + + while (!ss.eof()) { + Real x, y; + ss >> x; + ss >> y; + data.push_back({x,y}); + } + + unsigned M = data.size(); + + Rng r; + + std::cout << std::setprecision(15); + + for (unsigned N = 1; N <= M; N++) { + Vector a = underSolve(data, N); + + for (Real ai : a) { + std::cout << ai << " "; + } + std::cout << std::endl; + } + + for (unsigned N = Nend; N > M; N--) { + Vector a₀ = Vector::Zero(N); + for (Real& aa : a₀) { + aa = r.variate(0, iniVar); + } + + Vector a = stochasticGradientDescent(data, a₀, nBatches, maxSteps); + + for (Real ai : a) { + std::cout << ai << " "; + } + std::cout << std::endl; + } + + return 0; +} diff --git a/ictp-saifr_colloquium.tex b/ictp-saifr_colloquium.tex index 1fa3a0b..92b4904 100644 --- a/ictp-saifr_colloquium.tex +++ b/ictp-saifr_colloquium.tex @@ -426,11 +426,361 @@ \] \end{column} \begin{column}{0.5\textwidth} + \begin{overprint} + \onslide<1>\includegraphics[width=\columnwidth]{figs/fit_gradient_1.pdf} + \onslide<2>\includegraphics[width=\columnwidth]{figs/fit_gradient_2.pdf} + \onslide<3>\includegraphics[width=\columnwidth]{figs/fit_gradient_3.pdf} + \onslide<4>\includegraphics[width=\columnwidth]{figs/fit_gradient_4.pdf} + \onslide<5>\includegraphics[width=\columnwidth]{figs/fit_gradient_5.pdf} + \onslide<6>\includegraphics[width=\columnwidth]{figs/fit_gradient_6.pdf} + \end{overprint} + \end{column} + \end{columns} +\end{frame} + +\begin{frame} + \frametitle{Curve fitting: choice of basis} + + \begin{columns} + \begin{column}{0.5\textwidth} + \centering + \textbf{Polynomial basis} + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_basis_poly.pdf} + \end{column} + \begin{column}{0.5\textwidth} + \centering + \textbf{Absolute value basis} + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_basis_abs.pdf} \end{column} \end{columns} \end{frame} \begin{frame} + \frametitle{Curve fitting: choice of basis} + \centering + \Large\textbf{Polynomial basis}\normalsize + + \bigskip + + \begin{columns} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=2$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_underfit_poly.pdf} + + \bigskip + + Underfit + + \smallskip + + $\chi^2$ is large + + \smallskip + + Best fit has \emph{high bias} \phantom{variance} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=7$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_goodfit_poly.pdf} + + \bigskip + + Good fit! + + \smallskip + + $\chi^2$ is moderate + + \smallskip + + Best fit has \emph{low variance} and \emph{low bias} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=40$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_overfit_poly.pdf} + + \bigskip + + Overfit + + \smallskip + + $\chi^2$ is zero + + \smallskip + + Best fit has \emph{high variance} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=80$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_overparamfit_poly.pdf} + + \bigskip + + Good fit? + + \smallskip + + $\chi^2$ is zero + + \smallskip + + Best fit has \emph{low variance} and \emph{low bias} + \end{column} + \end{columns} +\end{frame} + +\begin{frame} + \frametitle{Curve fitting: choice of basis} + \centering + \Large\textbf{Absolute value basis\vphantom{y}}\normalsize + + \bigskip + + \begin{columns} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=2$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_underfit_abs.pdf} + + \bigskip + + Underfit + + \smallskip + + $\chi^2$ is large + + \smallskip + + Best fit has \emph{high bias} \phantom{variance} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=7$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_goodfit_abs.pdf} + + \bigskip + + Good fit! + + \smallskip + + $\chi^2$ is moderate + + \smallskip + + Best fit has \emph{low variance} and \emph{low bias} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=40$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_overfit_abs.pdf} + + \bigskip + + Good fit? + + \smallskip + + $\chi^2$ is zero + + \smallskip + + Best fit has \emph{low variance} and \emph{low bias} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=40$, $N=80$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_overparamfit_abs.pdf} + + \bigskip + + Good fit? + + \smallskip + + $\chi^2$ is zero + + \smallskip + + Best fit has \emph{low variance} and \emph{low bias} + \end{column} + \end{columns} +\end{frame} + +\begin{frame} + \frametitle{Curve fitting: choice of basis} + + \begin{columns} + \begin{column}{0.5\textwidth} + \centering + \textbf{Polynomial basis} + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_bias-variance2_poly.pdf} + \end{column} + \begin{column}{0.5\textwidth} + \centering + \textbf{Absolute value basis} + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_bias-variance_abs.pdf} + \end{column} + \end{columns} +\end{frame} + +\begin{frame} + \frametitle{Curve fitting: sparseness and level of noise} + + \begin{columns} + \begin{column}{0.5\textwidth} + \includegraphics[width=\columnwidth]{figs/fit_data.pdf} + \end{column} + \begin{column}{0.5\textwidth} + \includegraphics[width=\columnwidth]{figs/fit_data_abs2.pdf} + \end{column} + \end{columns} +\end{frame} + +\begin{frame} + \frametitle{Curve fitting: sparseness and level of noise} + \begin{columns} + \begin{column}{0.25\textwidth} + \centering + $M=10$, $N=4$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_underfit_abs2.pdf} + + \bigskip + + Underfit + + \smallskip + + $\chi^2$ is large + + \smallskip + + Best fit has \emph{high bias} \phantom{variance} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=10$, $N=6$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_goodfit_abs2.pdf} + + \bigskip + + Good fit! + + \smallskip + + $\chi^2$ is moderate + + \smallskip + + Best fit has \emph{low variance} and \emph{low bias} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=10$, $N=10$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_overfit_abs2.pdf} + + \bigskip + + Good fit? + + \smallskip + + $\chi^2$ is zero + + \smallskip + + Best fit has \emph{low variance} and \emph{low bias} + \end{column} + \begin{column}{0.25\textwidth} + \centering + $M=10$, $N=15$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_overparamfit_abs2.pdf} + + \bigskip + + Better fit?! + + \smallskip + + $\chi^2$ is zero + + \smallskip + + Best fit has \emph{low variance} and \emph{low bias} + \end{column} + \end{columns} +\end{frame} + +\begin{frame} + \frametitle{Curve fitting: sparseness and level of noise} + + \begin{columns} + \begin{column}{0.5\textwidth} + \centering + $M=10$, $N=15$ + + \bigskip + + \includegraphics[width=\columnwidth]{figs/fit_overparamfit_abs2.pdf} + \end{column} + \begin{column}{0.5\textwidth} + \includegraphics[width=\columnwidth]{figs/fit_bias-variance_abs2.pdf} + \end{column} + \end{columns} \end{frame} \begin{frame} diff --git a/test2.dat b/test2.dat 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