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It is known that homogeneous distribution of particles in Coulomb-like systems can be unstable, and spatially inhomogeneous structures can be formed. A simple method for describing such inhomogeneous systems and obtaining spacial…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
We sample a velocity field that has an inertial spectrum and a skewness that matches experimental data. In particular, we compute a self-consistent correction to the Kolmogorov exponent and find that for our model it is zero. We find that…
Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended…
For a finite word $w$ we define and study the Kolmogorov structure function $h_w$ for nondeterministic automatic complexity. We prove upper bounds on $h_w$ that appear to be quite sharp, based on numerical evidence.
We introduce a low dimensional function of the site frequency spectrum that is tailor-made for distinguishing coalescent models with multiple mergers from Kingman coalescent models with population growth, and use this function to construct…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
Estimation and counterfactual analysis in dynamic structural models rely on assumptions about the dynamic process of latent variables, which may be misspecified. We propose a framework to quantify the sensitivity of scalar parameters of…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
A striking consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of a bijection between the local density and the ground-state many-body wave function. Here we study the problem of constructing…
Forecasting is usually framed as a problem of model choice. This paper starts earlier, asking how much predictive information is available at each horizon. Under logarithmic loss, the answer is exact: the mutual information between the…
The rapid evolution of network services demands new paradigms for studying and designing networks. In order to understand the underlying mechanisms that provide network functions, we propose a framework which enables the functional analysis…
Convex functionals are ubiquitous in applied analysis, appearing as value functions, risk measures, super-hedging prices, and loss functionals in machine learning. In many applications, however, the functional is only observed through…
We propose a new way of thinking about deep neural networks, in which the linear and non-linear components of the network are naturally derived and justified in terms of principles in probability theory. In particular, the models…
We introduce new modified Abelian lattice models, with inhomogeneous local interactions, in which a sum over topological sectors are included in the defining partition function. The dual models, on lattices with arbitrary topology, are…
In this paper, we consider detecting and estimating breaks in heterogeneous mean functions of high-dimensional functional time series which are allowed to be cross-sectionally correlated and temporally dependent. A new test statistic…
A fundamental challenge in developing high-impact machine learning technologies is balancing the need to model rich, structured domains with the ability to scale to big data. Many important problem areas are both richly structured and large…
We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…
It is shown that in adiabatic approximation for nuclei the many-component Coulomb system cannot be described on the basis of the grand canonical ensemble. Using the variational Bogolyubov's procedure for the free energy, the Hohenberg-Kohn…