First draft of gzip classification presentation

static/src/gzip-classification.tex

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+\documentclass{beamer}
+
+\usepackage{pythonhighlight}
+
+% https://arxiv.org/abs/2212.09410
+% https://arxiv.org/abs/2309.10668
+% https://github.com/Futrell/ziplm
+% https://bellard.org/nncp/nncp_v2.1.pdf
+% https://prize.hutter1.net/ (blocked by AMD 🤷)
+% https://kenschutte.com/gzip-knn-paper/
+% https://kenschutte.com/gzip-knn-paper2/
+
+\title{Less is More: Parameter-Free Text Classification with Gzip}
+\author{Anthony Wang}
+
+\begin{document}
+
+\frame{\titlepage}
+
+\begin{frame}
+	\frametitle{Task: text compression}
+	\begin{itemize}
+		\item Given some 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}