Related papers: Streaming and Sublinear Approximation of Entropy a…
Motivated by the approach of random linear codes, a new distance in the vector space over a finite field is defined as the logarithm of the "surface area" of a Hamming ball with radius being the corresponding Hamming distance. It is named…
With the massive data challenges nowadays and the rapid growing of technology, stream mining has recently received considerable attention. To address the large number of scenarios in which this phenomenon manifests itself suitable tools are…
Diversity maximization is a fundamental problem with wide applications in data summarization, web search, and recommender systems. Given a set $X$ of $n$ elements, it asks to select a subset $S$ of $k \ll n$ elements with maximum…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
In insertion-only streaming, one sees a sequence of indices $a_1, a_2, \ldots, a_m\in [n]$. The stream defines a sequence of $m$ frequency vectors $x^{(1)},\ldots,x^{(m)}\in\mathbb{R}^n$ with $(x^{(t)})_i = |\{j : j\in[t], a_j = i\}|$. That…
The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example.…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
Monitoring the performance of large shared computing systems such as the cloud computing infrastructure raises many challenging algorithmic problems. One common problem is to track users with the largest deviation from the norm (outliers),…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…
Deep neural networks have consistently shown great performance in several real-world use cases like autonomous vehicles, satellite imaging, etc., effectively leveraging large corpora of labeled training data. However, learning unbiased…
A data stream model represents setting where approximating pairwise, or $k$-wise, independence with sublinear memory is of considerable importance. In the streaming model the joint distribution is given by a stream of $k$-tuples, with the…
Big data streams are possibly one of the most essential underlying notions. However, data streams are often challenging to handle owing to their rapid pace and limited information lifetime. It is difficult to collect and communicate stream…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
The histogram is a key method for visualizing data and estimating the underlying probability distribution. Incorrect conclusions about the data result from over or under-binning. A new method based on the Shannon entropy of the histogram…
Dimension is an inherent bottleneck to some modern learning tasks, where optimization methods suffer from the size of the data. In this paper, we study non-isotropic distributions of data and develop tools that aim at reducing these…
Gathering the most information by picking the least amount of data is a common task in experimental design or when exploring an unknown environment in reinforcement learning and robotics. A widely used measure for quantifying the…
Compression of documents, images, audios and videos have been traditionally practiced to increase the efficiency of data storage and transfer. However, in order to process or carry out any analytical computations, decompression has become…
A text stream is an ordered sequence of text documents generated over time. A massive amount of such text data is generated by online social platforms every day. Designing an algorithm for such text streams to extract useful information is…
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…
We design efficient distance approximation algorithms for several classes of structured high-dimensional distributions. Specifically, we show algorithms for the following problems: - Given sample access to two Bayesian networks $P_1$ and…