Related papers: Machine Learning of the Prime Distribution
We consider a new learning model in which a joint distribution over vector pairs $(x,y)$ is determined by an unknown function $c(x)$ that maps input vectors $x$ not to individual outputs, but to entire {\em distributions\/} over output…
Random walks are a common model for exploration and discovery of complex networks. While numerous algorithms have been proposed to map out an unknown network, a complementary question arises: in a known network, which nodes and edges are…
We consider the problem of distilling uniform random bits from an unknown source with a given $p$-entropy using linear hashing. As our main result, we estimate the expected $p$-divergence from the uniform distribution over the ensemble of…
This paper considers ranking inference of $n$ items based on the observed data on the top choice among $M$ randomly selected items at each trial. This is a useful modification of the Plackett-Luce model for $M$-way ranking with only the top…
The Rasch model has been widely used to analyse item response data in psychometrics and educational assessments. When the number of individuals and items are large, it may be impractical to provide all possible responses. It is desirable to…
We study the maximum of the random assignment process on rectangular matrices. We derive first-order asymptotics for the expected maximum, prove a law of large numbers under mild tail assumptions, and obtain exponential upper bounds for the…
We introduce a novel class of algorithms to efficiently approximate the unknown return distributions in policy evaluation problems from distributional reinforcement learning (DRL). The proposed distributional dynamic programming algorithms…
Inspired by applications to theories of coding and communication in networks of nervous tissue, we study maximum entropy distributions on weighted graphs with a given expected degree sequence. These distributions are characterized by…
In the pursuit of finding an optimal policy, reinforcement learning (RL) methods generally ignore the properties of learned policies apart from their expected return. Thus, even when successful, it is difficult to characterize which…
Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods,…
We study in limit law the complexity of some anticipated rejection random sampling algorithms. We express this complexity in terms of a probabilistic process, the threshold sum process. We show that, under the right conditions, the…
Maximum entropy reinforcement learning integrates exploration into policy learning by providing additional intrinsic rewards proportional to the entropy of some distribution. In this paper, we propose a novel approach in which the intrinsic…
We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated…
Machine learning theory has mostly focused on generalization to samples from the same distribution as the training data. Whereas a better understanding of generalization beyond the training distribution where the observed distribution…
We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator.…
Learning distributions over permutations is a fundamental problem in machine learning, with applications in ranking, combinatorial optimization, structured prediction, and data association. Existing methods rely on mixtures of parametric…
We introduce probabilistic neural networks that describe unsupervised synchronous learning on an atomic Hardy space and space of bounded real analytic functions, respectively. For a stationary ergodic vector process, we prove that the…
We find assimpotics for the first $k$ highest degrees of the degree distribution in an evolving tree model combining the local choice and the preferential attachment. In the considered model, the random graph is constructd in the following…
This paper is a survey of applications of the theory of algorithmic randomness to ergodic theory. We establish various degrees of constructivity for asymptotic laws of probability theory. In the framework of the Kolmogorov approach to the…
In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to…