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Stochastic gradient methods enable learning probabilistic models from large amounts of data. While large step-sizes (learning rates) have shown to be best for least-squares (e.g., Gaussian noise) once combined with parameter averaging,…
The processes, resulting in the transcription of RNA, are intrinsically noisy. It was observed experimentally that the synthesis of mRNA molecules is driven by short, burst-like, events. An accurate prediction of the protein level often…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…
We consider the modeling of the dynamics of the chemostat at its very source. The chemostat is classically represented as a system of ordinary differential equations. Our goal is to establish a stochastic model that is valid at the scale…
We present a self-consistent field approximation to the problem of the genetic switch composed of two mutually repressing/activating genes. The protein and DNA state dynamics are treated stochastically and on equal footing. In this approach…
Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
Mean field approximation is a powerful technique which has been used in many settings to study large-scale stochastic systems. In the case of two-timescale systems, the approximation is obtained by a combination of scaling arguments and the…
Simplified stochastic models are widely used in the study of frequency-resolved noise propagation in biochemical reaction networks, a common measure being the coherence between random fluctuations in molecule number trajectories. Such…
In this paper we consider approximations to the popular Pitman-Yor process obtained by truncating the stick-breaking representation. The truncation is determined by a random stopping rule that achieves an almost sure control on the…
The recent advancements in mathematical modeling of biochemical systems have generated increased interest in sensitivity analysis methodologies. There are two primary approaches for analyzing these mathematical models: the stochastic…
Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain. Applications include longitudinal medical image analysis with both population trends and random…
Observation of phenotypic diversity in a population of genetically identical cells is often linked to the stochastic nature of chemical reactions involved in gene regulatory networks. We investigate the distribution of population averaged…
We train a neural network to predict distributional responses in gene expression following genetic perturbations. This is an essential task in early-stage drug discovery, where such responses can offer insights into gene function and inform…
An important question in evolutionary computation is how good solutions evolutionary algorithms can produce. This paper aims to provide an analytic analysis of solution quality in terms of the relative approximation error, which is defined…
Genetic Programming has been very successful in solving a large area of problems but its use as a machine learning algorithm has been limited so far. One of the reasons is the problem of overfitting which cannot be solved or suppresed as…
In 1951 Robbins and Monro published the seminal article on stochastic approximation and made a specific reference to its application to the "estimation of a quantal using response, nonresponse data." Since the 1990s, statistical methodology…
We provide a unifying approximate dynamic programming framework that applies to a broad variety of problems involving sequential estimation. We consider first the construction of surrogate cost functions for the purposes of optimization,…
This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for…