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In this paper, we propose to model the video dynamics by learning the trajectory of independently inverted latent codes from GANs. The entire sequence is seen as discrete-time observations of a continuous trajectory of the initial latent…
Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of ordinary differential equations (ODEs). Alternative approaches based on formal calculi, often derived from process algebras or term…
Deep generative models aim to learn underlying distributions that generate the observed data. Given the fact that the generative distribution may be complex and intractable, deep latent variable models use probabilistic frameworks to learn…
Modeling the dynamics of probability distributions from time-dependent data samples is a fundamental problem in many fields, including digital health. The goal is to analyze how the distribution of a biomarker, such as glucose, changes over…
One of the major shortcomings of variational autoencoders is the inability to produce generations from the individual modalities of data originating from mixture distributions. This is primarily due to the use of a simple isotropic Gaussian…
Statistical analysis of DNA mixtures is known to pose computational challenges due to the enormous state space of possible DNA profiles. We propose a Bayesian network representation for genotypes, allowing computations to be performed…
Next-generation sequencing technologies now constitute a method of choice to measure gene expression. Data to analyze are read counts, commonly modeled using Negative Binomial distributions. A relevant issue associated with this…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…
Metabolic heterogeneity is widely recognised as the next challenge in our understanding of non-genetic variation. A growing body of evidence suggests that metabolic heterogeneity may result from the inherent stochasticity of intracellular…
We present Ordinary Differential Equation Variational Auto-Encoder (ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE$^2$VAE can simultaneously learn…
Ordinary differential equations (ODEs) are a mathematical model used in many application areas such as climatology, bioinformatics, and chemical engineering with its intuitive appeal to modeling. Despite ODE's wide usage in modeling, the…
Artificial neural networks, widely recognised for their role in machine learning, are now transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems and enabling the…
This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian…
Deep probabilistic time series forecasting models have become an integral part of machine learning. While several powerful generative models have been proposed, we provide evidence that their associated inference models are oftentimes too…
Time-course gene expression datasets provide insight into the dynamics of complex biological processes, such as immune response and organ development. It is of interest to identify genes with similar temporal expression patterns because…
Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on…
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…
Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we…
In this paper an analytic approach is devised to represent, and study the behavior of, nonlinear dynamic chaotic Genesio system using general nonlinear modal representation. In this approach, the original nonlinear ordinary differential…