Related papers: Maximum Probability Domains for Hubbard Models
We construct maximal $\Lambda(p)$-subsets on a large class of curved manifolds, in an optimal range of Lebesgue exponents $p$. Our arguments combine restriction estimates and decoupling with old and new probabilistic estimates.
We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD…
We construct the maximally predictable portfolio (MPP) of stocks using machine learning. Solving for the optimal constrained weights in the multi-asset MPP gives portfolios with a high monthly coefficient of determination, given the sample…
Continuous-time Markov processes over finite state-spaces are widely used to model dynamical processes in many fields of natural and social science. Here, we introduce an maximum likelihood estimator for constructing such models from data…
Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…
Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…
Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…
The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…
Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability,…
Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…
This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…
The maximum product of spacings (MPS) is employed in the estimation of the Generalized Extreme Value Distribution (GEV) and the Generalized Pareto Distribution (GPD). Efficient estimators are obtained by the MPS for all $\gamma$. This…
Monte Carlo maximum likelihood (MCML) provides an elegant approach to find maximum likelihood estimators (MLEs) for latent variable models. However, MCML algorithms are computationally expensive when the latent variables are…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger…
Model Predictive Control (MPC) is among the most widely adopted and reliable methods for robot control, relying critically on an accurate dynamics model. However, existing dynamics models used in the gradient-based MPC are limited by…
A challenge - and opportunity - is offered to the Hubbard Model community of solutions extant for the strong coupling region. A rigorous and quantitatively demanding test - a Computer Lab - is presented based on certain exact results for…
Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…
Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other. Such…