相关论文: Multiplicative Turing Ensembles, Pareto's Law, and…

Success in modeling complex phenomena such as human perception hinges critically on the availability of data and computational power. Significant progress has been made in modeling such phenomena using probabilistic methods, particularly in…

We present an efficient algorithm for maximum likelihood estimation (MLE) of exponential family models, with a general parametrization of the energy function that includes neural networks. We exploit the primal-dual view of the MLE with a…

In many applications expectation values are calculated by partitioning a single experimental time series into an ensemble of data segments of equal length. Such single trajectory ensemble (STE) is a counterpart to a multiple trajectory…

We introduce the well-tempered ensemble (WTE) which is the biased ensemble sampled by well-tempered metadynamics when the energy is used as collective variable. WTE can be designed so as to have approximately the same average energy as the…

Tree ensembles (TEs) find a multitude of practical applications. They represent one of the most general and accurate classes of machine learning methods. While they are typically quite concise in representation, their operation remains…

We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…

We develop a unified density-based framework for primality, coprimality, and prime pairs, and introduce an intrinsic normalized model for prime gaps constrained by the Prime Number Theorem. Within this setting, a structural tension between…

We introduce a Maximum Entropy model able to capture the statistics of melodies in music. The model can be used to generate new melodies that emulate the style of the musical corpus which was used to train it. Instead of using the $n-$body…

Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signalling an end of a calculation by setting a halt…

A Chaitin Omega number is the halting probability of a universal Chaitin (self-delimiting Turing) machine. Every Omega number is both computably enumerable (the limit of a computable, increasing, converging sequence of rationals) and random…

We characterize the biorthogonal ensembles that are both a multiple orthogonal polynomial ensemble and a polynomial ensemble of derivative type (also called a P\'olya ensemble). We focus on the notions of multiplicative and additive…

The infinite projected entangled pair states (iPEPS) technique [J. Jordan {\it et al.}, Phys. Rev. Lett. {\bf 101}, 250602 (2008)] has been widely used in the recent years to assess the properties of two-dimensional quantum systems, working…

We establish a prime number theorem for all uniquely ergodic, analytic skew products on the $2$-torus $\mathbb{T}^2$. More precisely, for every irrational $\alpha$ and every $1$-periodic real analytic $g:\mathbb{R}\to\mathbb{R}$ of zero…

We study exponential families of distributions that are multivariate totally positive of order 2 (MTP2), show that these are convex exponential families, and derive conditions for existence of the MLE. Quadratic exponential familes of MTP2…

The recent line of study on randomness extractors has been a great success, resulting in exciting new techniques, new connections, and breakthroughs to long standing open problems in several seemingly different topics. These include seeded…

This paper introduces a theoretical framework for a Transformer-augmented, sectional Mixture-of-Experts (MoE) architecture that aims to enhance computational efficiency while preserving model scalability. Unlike conventional MoE models,…

Systems driven by innovation, a pivotal force in human society, present various intriguing statistical regularities, from the Heaps' law to logarithmic scaling or somewhat different patterns for the innovation rates. The Urn Model with…

We advocate for a practical Maximum Likelihood Estimation (MLE) approach towards designing loss functions for regression and forecasting, as an alternative to the typical approach of direct empirical risk minimization on a specific target…

The serial concatenation of a repetition code with two or more accumulators has the advantage of a simple encoder structure. Furthermore, the resulting ensemble is asymptotically good and exhibits minimum distance growing linearly with…

This paper presents a new model for characterising temporal dependence in exceedances above a threshold. The model is based on the class of trawl processes, which are stationary, infinitely divisible stochastic processes. The model for…