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We introduce methods of characterizing entanglement, in which entanglement measures are enriched by the matrix representations of operators for observables. These observable operator matrix representations can enrich the partial trace over…
In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of {available data} and prior information. When the distribution of random variables is {intractable}, Monte Carlo (MC)…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…
This paper studies Kernel Density Estimation for a high-dimensional distribution $\rho(x)$. Traditional approaches have focused on the limit of large number of data points $n$ and fixed dimension $d$. We analyze instead the regime where…
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…
Understanding and comparing distributions of data (e.g., regarding their modes, shapes, or outliers) is a common challenge in many scientific disciplines. Typically, this challenge is addressed using side-by-side comparisons of histograms…
Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…
We study the selective learning problem introduced by Qiao and Valiant (2019), in which the learner observes $n$ labeled data points one at a time. At a time of its choosing, the learner selects a window length $w$ and a model $\hat\ell$…
We present EntropyDB, an interactive data exploration system that uses a probabilistic approach to generate a small, query-able summary of a dataset. Departing from traditional summarization techniques, we use the Principle of Maximum…
The supernova (SN) Hubble diagram residual contains valuable information on both the present matter power spectrum and its growth history. In this paper we show that this information can be retrieved with precision by combining both…
This work proposes a method for using any generator network as the foundation of an Energy-Based Model (EBM). Our formulation posits that observed images are the sum of unobserved latent variables passed through the generator network and a…
Motivated by the computational and storage challenges that dense embeddings pose, we introduce the problem of latent network summarization that aims to learn a compact, latent representation of the graph structure with dimensionality that…
This article introduces subbagging (subsample aggregating) estimation approaches for big data analysis with memory constraints of computers. Specifically, for the whole dataset with size $N$, $m_N$ subsamples are randomly drawn, and each…
Human mathematics (HM), the mathematics humans discover and value, is a vanishingly small subset of formal mathematics (FM), the totality of all valid deductions. We argue that HM is distinguished by its compressibility through…
A finite set is "hidden" if its elements are not directly enumerable or if its size cannot be ascertained via a deterministic query. In public health, epidemiology, demography, ecology and intelligence analysis, researchers have developed a…
Rapidly growing data sizes of scientific simulations pose significant challenges for interactive visualization and analysis techniques. In this work, we propose a compact probabilistic representation to interactively visualize large…
A detailed environment representation is a crucial component of automated vehicles. Using single range sensor scans, data is often too sparse and subject to occlusions. Therefore, we present a method to augment occupancy grid maps from…
Current constraints on models of galaxy evolution rely on morphometric catalogs extracted from multi-band photometric surveys. However, these catalogs are altered by selection effects that are difficult to model, that correlate in non…
Motivated by very large-scale communication networks, we newly introduce exponentiation of graphs. Using the exponential operation on graphs, we can construct various graphs of multi-exponential order with logarithmic diameter. We show that…