Related papers: Multiplicative Turing Ensembles, Pareto's Law, and…
Interactions among multiple time series of positive random variables are crucial in diverse financial applications, from spillover effects to volatility interdependence. A popular model in this setting is the vector Multiplicative Error…
We consider a family of determinantal random point processes on the two-dimensional lattice and prove that members of our family can be interpreted as a kind of Gibbs ensembles of nonintersecting paths. Examples include probability measures…
Deep generative models have emerged as a popular machine learning-based approach for inverse design problems in the life sciences. However, these problems often require sampling new designs that satisfy multiple properties of interest in…
This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete "names", possibly…
We propose a Gaussian ensemble as a description of the long-time dynamics of isolated quantum integrable systems. Our approach extends the Generalized Gibbs Ensemble (GGE) by incorporating fluctuations of integrals of motion. It is…
Ensembles improve prediction performance and allow uncertainty quantification by aggregating predictions from multiple models. In deep ensembling, the individual models are usually black box neural networks, or recently, partially…
Multiway Turing machines (also known as nondeterministic Turing machines or NDTMs) with explicit, simple rules are studied. Even very simple rules are found to generate complex behavior, characterized by complex multiway graphs, that can be…
An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness has received much attention in the model-based clustering literature recently, we investigate the use of a…
Meteorological ensembles are a collection of scenarios for future weather delivered by a meteorological center. Such ensembles form the main source of valuable information for probabilistic forecasting which aims at producing a predictive…
We study the distribution of the sequence of elements of the discrete dynamical system generated by iterations of the M\"obius map $x \mapsto (ax + b)/(cx+d)$ over a finite field of $p$ elements at the moments of time that correspond to…
The Mixture-of-Experts (MoE) architecture enables a significant increase in the total number of model parameters with minimal computational overhead. However, it is not clear what performance tradeoffs, if any, exist between MoEs and…
In 1975 Chaitin introduced his \Omega number as a concrete example of random real. The real \Omega is defined based on the set of all halting inputs for an optimal prefix-free machine U, which is a universal decoding algorithm used to…
Our main result is the martingale representations for Markov additive processes where the modulator is a Levy process. These processes have three parts: the modulator, the jumps of the ordinate triggered by the modulator, and the…
This is an expository article to accompany my two lectures at the CDM conference. I have used this an excuse to make public two sets of notes I had lying around, and also to put together a short reader's guide to some recent joint work with…
Evidence often grounds temporal probabilistic relational models over time, which makes reasoning infeasible. To counteract groundings over time and to keep reasoning polynomial by restoring a lifted representation, we present temporal…
Impact assessment of natural hazards requires the consideration of both extreme and non-extreme events. Extensive research has been conducted on the joint modeling of bulk and tail in univariate settings; however, the corresponding body of…
Integral projection models (IPMs) are widely used to study population growth and the dynamics of demographic structure (e.g. age and size distributions) within a population.These models use data on individuals' growth, survival, and…
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection.…
We consider large-scale linear inverse problems in Bayesian settings. We follow a recent line of work that applies the approximate message passing (AMP) framework to multi-processor (MP) computational systems, where each processor node…
We introduce active generation of Pareto sets (A-GPS), a new framework for online discrete black-box multi-objective optimization (MOO). A-GPS learns a generative model of the Pareto set that supports a-posteriori conditioning on user…