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Recent advances have established the identifiability of a directed acyclic graph (DAG) under additive noise models (ANMs), spurring the development of various causal discovery methods. However, most existing methods make restrictive model…
We propose a method to estimate the uncertainty of the outcome of an image classifier on a given input datum. Deep neural networks commonly used for image classification are deterministic maps from an input image to an output class. As…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
Given positive integers $a_1,..., a_n, t$, the fixed weight subset sum problem is to find a subset of the $a_i$ that sum to $t$, where the subset has a prescribed number of elements. It is this problem that underlies the security of modern…
The choice of the PageRank damping factor is not evident. The Google's choice for the value c=0.85 was a compromise between the true reflection of the Web structure and numerical efficiency. However, the Markov random walk on the original…
Distance well-defined graphs consist of connected undirected graphs, strongly connected directed graphs and strongly connected mixed graphs. Let $G$ be a distance well-defined graph, and let ${\sf D}(G)$ be the distance matrix of $G$.…
We establish a novel framework for learning a directed acyclic graph (DAG) when data are generated from a Gaussian, linear structural equation model. It consists of two parts: (1) introduce a permutation matrix as a new parameter within a…
The question of whether there is a logic that captures polynomial time is one of the main open problems in descriptive complexity theory and database theory. In 2010 Grohe showed that fixed point logic with counting captures polynomial time…
Recent work shows how offset-value coding speeds up database query execution, not only sorting but also duplicate removal and grouping (aggregation) in sorted streams, order-preserving exchange (shuffle), merge join, and more. It already…
This paper presents the novel approach towards table structure recognition by leveraging the guided anchors. The concept differs from current state-of-the-art approaches for table structure recognition that naively apply object detection…
In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behaviour of cellular automata, that the computational basis…
Learning the structure of directed acyclic graphs (DAGs) from observational data is a central problem in causal discovery, statistical signal processing, and machine learning. Under a linear Gaussian structural equation model (SEM) with…
Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…
We study structure learning for linear Gaussian SEMs in the presence of latent confounding. Existing continuous methods excel when errors are independent, while deconfounding-first pipelines rely on pervasive factor structure or…
Here I argue that the much-discussed Doomsday Argument (DA) has two flaws. Its mathematical flaw stems from applying frequentist probability or faulty Bayesian inference. Its conceptual flaw is assuming that Copernican uniformity applies to…
We study a design framework for robust, independently verifiable, and workload-balanced distributed algorithms working on a common input. An algorithm based on the framework is essentially a distributed encoding procedure for a…
A constant-rate encoder--decoder pair is presented for a fairly large family of two-dimensional (2-D) constraints. Encoding and decoding is done in a row-by-row manner, and is sliding-block decodable. Essentially, the 2-D constraint is…
Ancient mesoamerican cultures built a short ritual 260 day calendar and used it for daily routinary life. Using simple arithmetic calculations it is first shown that by forcing the introduction of the the fundamental number 13 to calculate…
Arithmetic coding is an essential class of coding techniques. One key issue of arithmetic encoding method is to predict the probability of the current coding symbol from its context, i.e., the preceding encoded symbols, which usually can be…
An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the arcs alternate between forward and backward arcs. An antidirected path is an antidirected trail where no vertex is repeated. We show that it is…