Related papers: A novel algebraic approach to time-reversible evol…
In evolutionary studies it is common to use phylogenetic trees to represent the evolutionary history of a set of species. However, in case the transfer of genes or other genetic information between the species or their ancestors has…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
The accurate prediction of biological features from genomic data is paramount for precision medicine and sustainable agriculture. For decades, neural network models have been widely popular in fields like computer vision, astrophysics and…
Real-world generalization, e.g., deciding to approach a never-seen-before animal, relies on contextual information as well as previous experiences. Such a seemingly easy behavioral choice requires the interplay of multiple neural…
Mixture autoregressive (MAR) models provide a flexible way to model time series with predictive distributions which depend on the recent history of the process and are able to accommodate asymmetry and multimodality. Bayesian inference for…
Providing machine learning (ML) over relational data is a mainstream requirement for data analytics systems. While almost all the ML tools require the input data to be presented as a single table, many datasets are multi-table, which forces…
Evolution is a process that is influenced by various environmental factors, e.g. the interactions between different species, genes, and biogeographical properties. Hence, it is interesting to study the combined evolutionary history of…
Since the advent of modern bioinformatics, the challenging, multifaceted problem of reconstructing phylogenetic history from biological sequences has hatched perennial statistical and algorithmic innovation. Studies of the phylogenetic…
Diffusion-based generative models represent a forefront direction in generative AI research today. Recent studies in physics have suggested that the renormalization group (RG) can be conceptualized as a diffusion process. This insight…
Structured, or tabular, data is the most common format in data science. While deep learning models have proven formidable in learning from unstructured data such as images or speech, they are less accurate than simpler approaches when…
Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…
Modern generative machine learning models demonstrate surprising ability to create realistic outputs far beyond their training data, such as photorealistic artwork, accurate protein structures, or conversational text. These successes…
Phylogenetic inference, the task of reconstructing how related sequences evolved from common ancestors, is a central objective in evolutionary genomics. The current state-of-the-art methods exploit probabilistic models of sequence evolution…
In this work, we formally prove that, under certain conditions, if a neural network is invariant to a finite group then its weights recover the Fourier transform on that group. This provides a mathematical explanation for the emergence of…
Let $F$ be an algebraically closed field of characteristic zero, and $G$ be a finite abelian group. If $A=\oplus_{g\in G} A_g$ is a $G$-graded algebra, we study degree-inverting involutions on $A$, i.e., involutions $*$ on $A$ satisfying…
Threshold Autoregressive (TAR) models have been widely used by statisticians for non-linear time series forecasting during the past few decades, due to their simplicity and mathematical properties. On the other hand, in the forecasting…
We survey the development and status quo of a subject best described as "generic representation theory of finite dimensional algebras", which started taking shape in the early 1980s. Let $\Lambda$ be a finite dimensional algebra over an…
This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…
Homogeneity across lineages is a common assumption in phylogenetics according to which nucleotide substitution rates remain constant in time and do not depend on lineages. This is a simplifying hypothesis which is often adopted to make the…
This note places into perspective the so-called algebraic time-derivative estimation method recently introduced by Fliess and co-authors with standard results from linear state-space theory for control systems. In particular, it is shown…