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When the process underlying DNA substitutions varies across evolutionary history, the standard Markov models underlying standard phylogenetic methods are mathematically inconsistent. The most prominent example is the general time reversible…
Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…
In the last years, algebraic tools have been proven useful in phylogenetic reconstruction and model selection through the study of phylogenetic invariants. However, up to now, the models studied from an algebraic viewpoint are either too…
Models of random phylogenetic networks have been used since the inception of the field, but the introduction and rigorous study of mathematically tractable models is a much more recent topic that has gained momentum in the last 5 years.…
Generative machine learning models can use data generated by scientific modeling to create large quantities of novel material structures. Here, we assess how one state-of-the-art generative model, the physics-guided crystal generation model…
Inference of evolutionary trees and rates from biological sequences is commonly performed using continuous-time Markov models of character change. The Markov process evolves along an unknown tree while observations arise only from the tips…
Despite recent progress in time-series foundation models, challenges persist in improving representation learning and adapting to diverse downstream tasks. We introduce a General Time-series Model (GTM), which advances representation…
Lateral gene transfer (LGT) is a common mechanism of non-vertical evolution where genetic material is transferred between two more or less distantly related organisms. It is particularly common in bacteria where it contributes to adaptive…
Time series synthesis is an important research topic in the field of deep learning, which can be used for data augmentation. Time series data types can be broadly classified into regular or irregular. However, there are no existing…
Kernel Regularized Least Squares (KRLS) is a popular method for flexibly estimating models that may have complex relationships between variables. However, its usefulness to many researchers is limited for two reasons. First, existing…
Fitting generative models to sequential data typically involves two recursive computations through time, one forward and one backward. The latter could be a computation of the loss gradient (as in backpropagation through time), or an…
Grey system theory is an important mathematical tool for describing uncertain information in the real world. It has been used to solve the uncertainty problems specially caused by lack of information. As a novel theory, the theory can deal…
Latent structure methods, specifically linear continuous latent structure methods, are a type of fundamental statistical learning strategy. They are widely used for dimension reduction, regression and prediction, in the fields of…
Microstructural materials design is one of the most important applications of inverse modeling in materials science. Generally speaking, there are two broad modeling paradigms in scientific applications: forward and inverse. While the…
We consider the general problem of modeling temporal data with long-range dependencies, wherein new observations are fully or partially predictable based on temporally-distant, past observations. A sufficiently powerful temporal model…
The Grey System Theory (GST) is a powerful mathematical framework employed for modeling systems with uncertain or incomplete information. This paper proposes an integration of the GST with time scales, a generalized approach that…
Large-scale pre-training has recently emerged as a technique for creating capable, general purpose, generative models such as GPT-3, Megatron-Turing NLG, Gopher, and many others. In this paper, we highlight a counterintuitive property of…
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,…
The Wright-Fisher model is the most popular population model for describing the behaviour of evolutionary systems with a finite population size. Approximations to the model have commonly been used for the analysis of time-resolved genome…
In this article, a generalized inverse xgamma distribution (GIXGD) has been introduced as the generalized version of the inverse xgamma distribution. The proposed model exhibits the pattern of non-monotone hazard rate and belongs to family…