Related papers: Extractors for Sum of Two Sources
Motivated by practical generalizations of the classic $k$-median and $k$-means objectives, such as clustering with size constraints, fair clustering, and Wasserstein barycenter, we introduce a meta-theorem for designing coresets for…
It is well understood that if one is given a set $X \subset [0,1]$ of $n$ independent uniformly distributed random variables, then $$ \sup_{0 \leq x \leq 1} \left| \frac{\# X \cap [0,x]}{\# X} - x \right| \lesssim \frac{\sqrt{\log{n}}}{…
We present preliminary results from our on-going study: Comparing and optimizing source detection procedures for XMM images. By constructing realistic spatial and spectral source distributions and ``observing'' these through the XMM Science…
Creating labeled natural language training data is expensive and requires significant human effort. We mine input output examples from large corpora using a supervised mining function trained using a small seed set of only 100 examples. The…
This work introduces two new techniques for random number generation with any prescribed nonlinear distribution based on the k-vector methodology. The first approach is based on inverse transform sampling using the optimal k-vector to…
Subset-sum problems belong to the NP class and play an important role in both complexity theory and knapsack-based cryptosystems, which have been proved in the literature to become hardest when the so-called density approaches one. Lattice…
This paper introduces a unified framework for the detection of a source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver. The Generalized Maximum…
In this paper, we put forward the model of zero-error distributed function compression system of two binary memoryless sources X and Y, where there are two encoders En1 and En2 and one decoder De, connected by two channels (En1, De) and…
We propose a new approach to generate multiple variants of the target summary with diverse content and varying lengths, then score and select admissible ones according to users' needs. Abstractive summarizers trained on single reference…
Given two identical linear codes $\mathcal C$ over $\mathbb F_q$ of length $n$, we independently pick one codeword from each codebook uniformly at random. A $\textit{sumset}$ is formed by adding these two codewords entry-wise as integer…
We address the problem of distributed computation of arbitrary functions of two correlated sources $X_1$ and $X_2$, residing in two distributed source nodes, respectively. We exploit the structure of a computation task by coding source…
Thanks to the rise of wearable and connected devices, sensor-generated time series comprise a large and growing fraction of the world's data. Unfortunately, extracting value from this data can be challenging, since sensors report low-level…
It is well established that the notion of min-entropy fails to satisfy the \emph{chain rule} of the form $H(X,Y) = H(X|Y)+H(Y)$, known for Shannon Entropy. Such a property would help to analyze how min-entropy is split among smaller blocks.…
Curve samplers are sampling algorithms that proceed by viewing the domain as a vector space over a finite field, and randomly picking a low-degree curve in it as the sample. Curve samplers exhibit a nice property besides the sampling…
Selecting a bundle of items that collectively satisfies constraints is a fundamental task across databases, recommender systems, and text summarization. Unlike traditional retrieval that returns individual or top-k items, bundle retrieval…
We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…
Anomalous sound detection systems must detect unknown, atypical sounds using only normal audio data. Conventional methods use the serial method, a combination of outlier exposure (OE), which classifies normal and pseudo-anomalous data and…
Given a large set $U$ where each item $a\in U$ has weight $w(a)$, we want to estimate the total weight $W=\sum_{a\in U} w(a)$ to within factor of $1\pm\varepsilon$ with some constant probability $>1/2$. Since $n=|U|$ is large, we want to do…
Shannon entropy is the shortest average codeword length a lossless compressor can achieve by encoding i.i.d. symbols. However, there are cases in which the objective is to minimize the \textit{exponential} average codeword length, i.e. when…
Uniform sampling is a highly efficient method for data summarization. However, its effectiveness in producing coresets for clustering problems is not yet well understood, primarily because it generally does not yield a strong coreset, which…