Related papers: Plans D'Experiences D'Information De Kullback-Leib…
Incorporating information about the target distribution in proposal mechanisms generally produces efficient Markov chain Monte Carlo algorithms (or at least, algorithms that are more efficient than uninformed counterparts). For instance, it…
We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…
This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
Systems with both quantitative and qualitative responses are widely encountered in many applications. Design of experiment methods are needed when experiments are conducted to study such systems. Classic experimental design methods are…
The analysis of observed time series from nonlinear systems is usually done by making a time-delay reconstruction to unfold the dynamics on a multi-dimensional state space. An important aspect of the analysis is the choice of the correct…
The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…
We show that the predicted probability distributions for any $N$-parameter statistical model taking the form of an exponential family can be explicitly and analytically embedded isometrically in a $N{+}N$-dimensional Minkowski space. That…
Simulation design is the choice of locations in parameter space at which simulations are to be run and is the first step in building an emulator capable of quickly providing estimates of simulation results for arbitrary locations in the…
In this paper we formulate in general terms an approach to prove strong consistency of the Empirical Risk Minimisation inductive principle applied to the prototype or distance based clustering. This approach was motivated by the Divisive…
Space-filling experimental designs are widely used in engineering computer experiments, where only a limited number of expensive model evaluations can be afforded. Distance-based designs such as Maximin or Minimax ensure global…
Most psychophysical experiments discard half the data collected. Specifically, experiments discard reaction time data, and use binary responses (e.g. yes/no) to measure performance. Here, Shannon's information theory is used to define…
In this paper, we present a novel method for computing the relative entropy as well as the expected relative entropy using an MCMC chain. The relative entropy from information theory can be used to quantify differences in posterior…
Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…
The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in…
Space-filling designs are important in computer experiments, which are critical for building a cheap surrogate model that adequately approximates an expensive computer code. Many design construction techniques in the existing literature are…
It has been argued persuasively that, in order to evaluate climate models, the probability distributions of model output need to be compared to the corresponding empirical distributions of observed data. Distance measures between…
This paper presents methods for analyzing spatial experiments when complex spillovers, displacement effects, and other types of "interference" are present. We present a robust, design-based approach to analyzing effects in such settings.…
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…