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We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively…
We present a statistical mechanics approach to the protein folding problem. We first review some of the basic properties of proteins, and introduce some physical models to describe their thermodynamics. These models rely on a random…
Understanding centennial scale climate variability requires data sets that are accurate, long, continuous and of broad spatial coverage. Since instrumental measurements are generally only available after 1850, temperature fields must be…
This paper proposes a general framework for internal patch-based image restoration based on Conditional Random Fields (CRF). Unlike related models based on Markov Random Fields (MRF), our approach explicitly formulates the posterior…
In modern scientific research, the objective is often to identify which variables are associated with an outcome among a large class of potential predictors. This goal can be achieved by selecting variables in a manner that controls the the…
Despite many advances in computational modeling of protein structures, these methods have not been widely utilized by experimental structural biologists. Two major obstacles are preventing the transition from a purely-experimental to a…
We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying…
A restricted Boltzmann machine (RBM) is an undirected graphical model constructed for discrete or continuous random variables, with two layers, one hidden and one visible, and no conditional dependency within a layer. In recent years, RBMs…
Effective protein representation learning is crucial for predicting protein functions. Traditional methods often pretrain protein language models on large, unlabeled amino acid sequences, followed by finetuning on labeled data. While…
Gibbs random fields (GRF) are polymorphous statistical models that can be used to analyse different types of dependence, in particular for spatially correlated data. However, when those models are faced with the challenge of selecting a…
Conformal inference is a statistical method used to construct prediction sets for point predictors, providing reliable uncertainty quantification with probability guarantees. This method utilizes historical labeled data to estimate the…
Recent advances in coarse-grained lattice and off-lattice protein models are reviewed. The sequence dependence of thermodynamical folding properties are investigated and evidence for non-randomness of the binary sequences of good folders…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
The most popular and universally predictive protein simulation models employ all-atom molecular dynamics (MD), but they come at extreme computational cost. The development of a universal, computationally efficient coarse-grained (CG) model…
We propose a flexible prior model for the parameters of binary Markov random fields (MRF) defined on rectangular lattices and with maximal cliques defined from a template maximal clique. The prior model allows higher-order interactions to…
The hidden Markov model (HMM) is a generative model that treats sequential data under the assumption that each observation is conditioned on the state of a discrete hidden variable that evolves in time as a Markov chain. In this paper, we…
Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…
Are we using the right potential functions in the Conditional Random Field models that are popular in the Vision community? Semantic segmentation and other pixel-level labelling tasks have made significant progress recently due to the deep…
The linear-chain Conditional Random Field (CRF) model is one of the most widely-used neural sequence labeling approaches. Exact probabilistic inference algorithms such as the forward-backward and Viterbi algorithms are typically applied in…
Scripts have been proposed to model the stereotypical event sequences found in narratives. They can be applied to make a variety of inferences including filling gaps in the narratives and resolving ambiguous references. This paper proposes…