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Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. Coherently defined feature representations must depend on the values in unobserved…
This study presents the approach to analyzing the evolution of an arbitrary complex system whose behavior is characterized by a set of different time-dependent factors. The key requirement for these factors is only that they must contain an…
In molecular phylogeny, relationships among organisms are reconstructed using DNA or protein sequences and are displayed as trees. A linear increase in the number of sequences results in an exponential increase of possible trees. Thus,…
A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…
Generative methods (Gen-AI) are reviewed with a particular goal of solving tasks in machine learning and Bayesian inference. Generative models require one to simulate a large training dataset and to use deep neural networks to solve a…
In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a…
Phylogenetic inference-the derivation of a hypothesis for the common evolutionary history of a group of species- is an active area of research at the intersection of biology, computer science, mathematics, and statistics. One assumes the…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…
Generative adversarial networks (GANs) are very popular to generate realistic images, but they often suffer from the training instability issues and the phenomenon of mode loss. In order to attain greater diversity in GAN synthesized data,…
Ancestral sequence reconstruction is a key task in computational biology. It consists in inferring a molecular sequence at an ancestral species of a known phylogeny, given descendant sequences at the tip of the tree. In addition to its many…
We address phylogenetic reconstruction when the data is generated from a mixture distribution. Such topics have gained considerable attention in the biological community with the clear evidence of heterogeneity of mutation rates. In our…
Many practical modeling problems involve discrete data that are best represented as draws from multinomial or categorical distributions. For example, nucleotides in a DNA sequence, children's names in a given state and year, and text…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the…
Understanding the dynamics of genome rearrangements is a major issue of phylogenetics. Phylogenetics is the study of species evolution. A major goal of the field is to establish evolutionary relationships within groups of species, in order…
Background: Continuous traits evolution of a group of taxa that are correlated through a phylogenetic tree is commonly modelled using parametric stochastic differential equations to represent deterministic change of trait through time,…
We observe $n$ sequences at each of $m$ sites, and assume that they have evolved from an ancestral sequence that forms the root of a binary tree of known topology and branch lengths, but the sequence states at internal nodes are unknown.…
Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially…