Related papers: An algorithmic and a geometric characterization of…
We show that the class of conditional distributions satisfying the coarsening at random (CAR) property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers: combinatorial objects…
In recent years a popular nonparametric model for coarsened data is an assumption on the coarsening mechanism called coarsening at random (CAR). It has been conjectured in several papers that this assumption cannot be tested by the data,…
We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…
Conditional auto-regressive (CAR) distributions are widely used to induce spatial dependence in the geographic analysis of areal data. These distributions establish multivariate dependence networks by defining conditional relationships…
A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…
Standard supervised learning optimizes for predictive accuracy but remains agnostic to the internal geometry of learned features, often yielding representations that are entangled and brittle. We propose Class-Conditional Activation…
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…
Causal Abstraction (CA) theory provides a principled framework for relating causal models that describe the same system at different levels of granularity while ensuring interventional consistency between them. Recent methods for learning…
The Heard-Of model is a simple and relatively expressive model of distributed computation. Because of this, it has gained a considerable attention of the verification community. We give a characterization of all algorithms solving consensus…
We propose a new geometric method for measuring the quality of representations obtained from deep learning. Our approach, called Random Polytope Descriptor, provides an efficient description of data points based on the construction of…
We clarify relationships between conditional (CAR) and simultaneous (SAR) autoregressive models. We review the literature on this topic and find that it is mostly incomplete. Our main result is that a SAR model can be written as a unique…
In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A…
The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…
We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather,…
How much can randomness help computation? Motivated by this general question and by volume computation, one of the few instances where randomness provably helps, we analyze a notion of dispersion and connect it to asymptotic convex…
Covariate-adaptive randomization (CAR) procedures are frequently used in comparative studies to increase the covariate balance across treatment groups. However, because randomization inevitably uses the covariate information when forming…
We study generalised additive models, with shape restrictions (e.g. monotonicity, convexity, concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a nonparametric estimator of each…