Related papers: Machine Learning of the Prime Distribution
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
On-line learning of probability distributions is analyzed from the field theoretical point of view. We can obtain an optimal on-line learning algorithm, since renormalization group enables us to control the number of degrees of freedom of a…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
We generalize current known distribution results on Shanks--R\'enyi prime number races to the case where arbitrarily many residue classes are involved. Our method handles both the classical case that goes back to Chebyshev and function…
In the online prediction framework, we use generalized entropy of to study the loss rate of predictors when outcomes are drawn according to stationary ergodic distributions over the binary alphabet. We show that the notion of generalized…
Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with…
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\{p_k\}$ for situations in…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
This work studies the distributed learning process on a network of agents. Agents make partial observation about an unknown hypothesis and iteratively share their beliefs over a set of possible hypotheses with their neighbors to learn the…
Maximum entropy (MAXENT) method has a large number of applications in theoretical and applied machine learning, since it provides a convenient non-parametric tool for estimating unknown probabilities. The method is a major contribution of…
We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of value of interactions and satisfaction as generic network performance measures, we show that…
We study the problem of estimating the \emph{value} of the largest mean among K distributions via samples from them (rather than estimating \emph{which} distribution has the largest mean), which arises from various machine learning tasks…
The vast majority of theoretical results in machine learning and statistics assume that the available training data is a reasonably reliable reflection of the phenomena to be learned or estimated. Similarly, the majority of machine learning…
We overview some results on distributed learning with focus on a family of recently proposed algorithms known as non-Bayesian social learning. We consider different approaches to the distributed learning problem and its algorithmic…
The lottery ticket hypothesis (LTH) has attracted attention because it can explain why over-parameterized models often show high generalization ability. It is known that when we use iterative magnitude pruning (IMP), which is an algorithm…
The "fire together, wire together" Hebbian model is a central principle for learning in neuroscience, but surprisingly, it has found limited applicability in modern machine learning. In this paper, we take a first step towards bridging this…
The results of the study provide guidelines for the development and applications of algorithms. When the number of steps for calculating an assumption tends to infinity, probability theory can be applied to predict whether the assumption…
We consider a problem where multiple agents must learn an action profile that maximises the sum of their utilities in a distributed manner. The agents are assumed to have no knowledge of either the utility functions or the actions and…
Machine-learning techniques have become fundamental in high-energy physics and, for new physics searches, it is crucial to know their performance in terms of experimental sensitivity, understood as the statistical significance of the…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…