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The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer,…
Recent inductive logic programming (ILP) approaches learn optimal hypotheses. An optimal hypothesis minimises a given cost function on the training data. There are many cost functions, such as minimising training error, textual complexity,…
Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…
Integer programming (IP) has proven to be highly effective in solving many path-based optimization problems in robotics. However, the applications of IP are generally done in an ad-hoc, problem specific manner. In this work, after examined…
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
Using recent results from the theory of integer points close to smooth curves, we give an asymptotic formula for the distribution of values of a class of integer-valued prime-independent multiplicative functions.
We provide a discussion of several recent results which, in certain scenarios, are able to overcome a barrier in distributed stochastic optimization for machine learning. Our focus is the so-called asymptotic network independence property,…
We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard…
We consider the problem of optimally locating a given number $k$ of points in ${\mathbb R}^n$ for an integral cost function which takes into account two measures $\varphi^+$ and $\varphi^-$. The points represent for example new industrial…
The multi-user linearly-separable distributed computing problem is considered here, in which $N$ servers help to compute the real-valued functions requested by $K$ users, where each function can be written as a linear combination of up to…
The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…
We obtain new transference bounds that connect two active areas of research: proximity and sparsity of solutions to integer programs. Specifically, we study the additive integrality gap of the integer linear programs min{cx: x in P, x…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
In distributed optimization for large-scale learning, a major performance limitation comes from the communications between the different entities. When computations are performed by workers on local data while a coordinator machine…
Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…
Approximate statistical inference via determination of the asymptotic distribution of a statistic is routinely used for inference in applied medical statistics (e.g. to estimate the standard error of the marginal or conditional risk ratio).…
We derive information-theoretic converses (i.e., lower bounds) for the minimum time required by any algorithm for distributed function computation over a network of point-to-point channels with finite capacity, where each node of the…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
In this work we study loss functions for learning and evaluating probability distributions over large discrete domains. Unlike classification or regression where a wide variety of loss functions are used, in the distribution learning and…