From 66432b3158c2182762572649ba0f051bf18dcaa6 Mon Sep 17 00:00:00 2001 From: Anthony Wang Date: Thu, 13 Jun 2024 17:57:31 -0500 Subject: [PATCH] First draft of gzip classification presentation --- static/src/gzip-classification.pdf | Bin 0 -> 115204 bytes static/src/gzip-classification.tex | 129 +++++++++++++++++++++++++++++ 2 files changed, 129 insertions(+) create mode 100644 static/src/gzip-classification.pdf create mode 100644 static/src/gzip-classification.tex diff --git a/static/src/gzip-classification.pdf b/static/src/gzip-classification.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8bf0d2cc070ea75e7074a05ec8c6099b21161a3a GIT binary patch literal 115204 zcmb5VW0Yjuwk@2tZB{z7(zb2ewr$(CDs9`gtx8wg&irzpd+&RvefzZc_KOuQ+Kl+I zVzoK@=(Eq!#~_gt5}~30$qYp@yEwE8#mGcJM__AU0ma1yMJr`&W9no^z{bEt@Lw+| zS`l+ACu0W!S`jOKCu1RFLt7(bC>|atM<)kkeQPMU^(7TaTV#5K?qk(Sdt$^DL(h+0 zurQT!z5?qaJU_uks|_(}iNrjho*YchN1H?l4O9&*3Qo?QX|J46U8HIL{ysh%u^-_- 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categories, classify strings into the categories + \item Example from AG News dataset: + \begin{itemize} + \item Categories: World, Sports, Business, Sci/Tech + \item Example string: "AMD Will Have An Edge Over Intel Through 2005. Piper Jaffray said Advanced Micro Devices (nyse: AMD - news - people ) should have an edge over Intel (nasdaq: INTC - news - people ) quot;throughout 2005 quot; but resumed coverage of both companies at quot;market perform quot; and both at price targets of \$25." + \end{itemize} + \item Usually solved using neural networks, i.e. BERT + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{gzip} + \begin{itemize} + \item Compression program using LZ77 and Huffman coding + \item Pretty fast and used everywhere + \item Doesn't require giant GPUs + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Intuition} + \begin{itemize} + \item Compressors are good at capturing regularity + \item Objects from the same category share more regularity than those that aren't + \item Compressor $C$, strings $x,y$ similar, different from $z$ + \item Then $C(xy) < C(xz)$ + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Kolmogorov complexity} + \begin{definition} + \textbf{Kolmogorov complexity} $K(x)$: length of shortest program that outputs $x$, i.e. an ideal compressor + \end{definition} + \begin{definition} + \textbf{Information distance} $E(x, y)$: length of shortest program that converts $x$ to $y$, equal to $K(xy)-K(x)$ + \end{definition} + \begin{itemize} + \item $K(x)$ is generally \textbf{incomputable} though, similar to the halting problem + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Approximating $K$} + \begin{itemize} + \item Simply swap out $K$ for our gzip compressor $C$ + \item Normalize by length + \end{itemize} + \begin{definition} + \textbf{Normalized compression distance} \[NCD(x,y) = \frac{C(x,y)-\min(C(x),C(y))}{\max(C(x),C(y))}\] + \end{definition} +\end{frame} + +\begin{frame} + \frametitle{Method for classification} + \begin{itemize} + \item $k$-nearest-neighbor among all strings in the training set, using $NCD$ as the distance + \item That's all! + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Code} + \begin{python} +from gzip import compress as C +import numpy as np + +for (x1, _) in test_set: + Cx1 = len(C(x1.encode())) + distance_from_x1 = [] + for (x2, _) in training_set: + Cx2 = len(C(x2.encode())) + x1x2 = " ".join([x1, x2]) + Cx1x2 = len(C(x1x2.encode())) + ncd = (Cx1x2 - min(Cx1,Cx2)) / max(Cx1, Cx2) + distance_from_x1.append(ncd) + sorted_idx = np.argsort(np.array(distance_from_x1)) + top_k_class = training_set[sorted_idx[:k], 1] + predict_class = max(set(top_k_class), key=top_k_class.count) + \end{python} +\end{frame} + +\begin{frame} + \frametitle{Performance optimizations} + \begin{itemize} + \item Can reuse $C(x)$ when computing $C(xy)$ + \item Multithreading + \item Use C instead of Python + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Results} +\end{frame} + +\begin{frame} + \frametitle{Actually\dots} +\end{frame} + +\begin{frame} + \frametitle{Connections between compression and ML} + \begin{itemize} + \item Autoencoders + \end{itemize} +\end{frame} + +\end{document}