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The quest to understand structure-function relationships in networks across scientific disciplines has intensified. However, the optimal network architecture remains elusive, particularly for complex information processing. Therefore, we…
We introduce a theoretical and practical framework for efficient importance sampling of mini-batch samples for gradient estimation from single and multiple probability distributions. To handle noisy gradients, our framework dynamically…
This paper investigates a change-point estimation problem in the context of high-dimensional Markov Random Field models. Change-points represent a key feature in many dynamically evolving network structures. The change-point estimate is…
In this paper we consider the convergence of the conditional entropy to the entropy rate for Markov chains. Convergence of certain statistics of long range dependent processes, such as the sample mean, is slow. It has been shown in Carpio…
Let x and y be two length n DNA sequences, and suppose we would like to estimate the divergence time T. A well known simple but crude estimate of T is p := d(x,y)/n, the fraction of mutated sites (the p-distance). We establish a posterior…
We present a comprehensive new framework for handling biologically accurate models of molecular evolution. This model provides a systematic framework for studying models of molecular evolution that implement heterogeneous rates,…
The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard…
A crucial assumption underlying the most current theory of machine learning is that the training distribution is identical to the test distribution. However, this assumption may not hold in some real-world applications. In this paper, we…
The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture.…
With this paper, we contribute to the growing research area of feature-based analysis of bio-inspired computing. In this research area, problem instances are classified according to different features of the underlying problem in terms of…
By providing a framework of accounting for the shared ancestry inherent to all life, phylogenetics is becoming the statistical foundation of biology. The importance of model choice continues to grow as phylogenetic models continue to…
Discriminating between competing explanatory models as to which is more likely responsible for the growth of a network is a problem of fundamental importance for network science. The rules governing this growth are attributed to mechanisms…
We introduce and analyze a waiting time model for the accumulation of genetic changes. The continuous time conjunctive Bayesian network is defined by a partially ordered set of mutations and by the rate of fixation of each mutation. The…
Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…
We present an algorithm for marginalising changepoints in time-series models that assume a fixed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables…
Probability density function estimation with weighted samples is the main foundation of all adaptive importance sampling algorithms. Classically, a target distribution is approximated either by a non-parametric model or within a parametric…
Adaptive importance sampling (AIS) algorithms are a rising methodology in signal processing, statistics, and machine learning. An effective adaptation of the proposals is key for the success of AIS. Recent works have shown that gradient…
Feature importance scores are ubiquitous tools for understanding the predictions of machine learning models. However, many popular attribution methods suffer from high instability due to random sampling. Leveraging novel ideas from…
The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…