arXiv subjects

Samir Bhatt

Publications and source records attributed to Samir Bhatt.

At least 37 records · Page 2Linked to original sources

arXiv2025

Inhomogeneous branching trees with symmetric and asymmetric offspring and their genealogies

We define symmetric and asymmetric branching trees, a class of processes particularly suited for modeling genealogies of inhomogeneous populations where individuals may reproduce throughout life. In this framework, a broad class of Crump-Mode-Jagers processes can be constructed as (a)symmetric Sevast'yanov processes, which count the branches of the tree. Analogous definitions yield reduced (a)symmetric Sevast'yanov processes, which restrict attention to branches that lead to extant progeny. We characterize their laws through generating functions. The genealogy obtained by pruning away branches without extant progeny at a fixed time is shown to satisfy a branching property, which provides distributional characterizations of the genealogy.

math.PR↗

arXiv2025

phylo2vec: a library for vector-based phylogenetic tree manipulation

Phylogenetics is a fundamental component of evolutionary analysis frameworks in biology and linguistics. Recently, the advent of large-scale genomics and the SARS-CoV-2 pandemic has highlighted the necessity for phylogenetic software to handle large datasets. While significant efforts have focused on scaling optimisation algorithms, visualization, and lineage identification, an emerging body of research has been dedicated to efficient representations of data for genomes and phylogenetic trees. Compared to the traditional Newick format which represents trees using strings of nested parentheses, modern tree representations utilize integer vectors to define the tree topology traversal. This approach offers several advantages, including easier manipulation, increased memory efficiency, and applicability to machine learning. Here, we present the latest release of phylo2vec (or Phylo2Vec), a high-performance software package for encoding, manipulating, and analysing binary phylogenetic trees. At its core, the package is based on the phylo2vec representation of binary trees, and is designed to enable fast sampling and tree comparison. This release features a core implementation in Rust for improved performance and memory efficiency, with wrappers in R and Python (superseding the original release), making it accessible to a broad audience in the bioinformatics community.

q-bio.PE↗

arXiv2025

Recurrent Memory for Online Interdomain Gaussian Processes

We propose a novel online Gaussian process (GP) model that is capable of capturing long-term memory in sequential data in an online learning setting. Our model, Online HiPPO Sparse Variational Gaussian Process (OHSVGP), leverages the HiPPO (High-order Polynomial Projection Operators) framework, which is popularized in the RNN domain due to its long-range memory modeling capabilities. We interpret the HiPPO time-varying orthogonal projections as inducing variables with time-dependent orthogonal polynomial basis functions, which allows the SVGP inducing variables to memorize the process history. We show that the HiPPO framework fits naturally into the interdomain GP framework and demonstrate that the kernel matrices can also be updated online in a recurrence form based on the ODE evolution of HiPPO. We evaluate OHSVGP with online prediction for 1D time series, continual learning in discriminative GP model for data with multidimensional inputs, and deep generative modeling with sparse Gaussian process variational autoencoder, showing that it outperforms existing online GP methods in terms of predictive performance, long-term memory preservation, and computational efficiency.

cs.LG↗

arXiv2025

Dynamic Graph-Based Forecasts of Bookmakers' Odds in Professional Tennis

Bookmakers' odds consistently provide one of the most accurate methods for predicting the results of professional tennis matches. However, these odds usually only become available shortly before a match takes place, limiting their usefulness as an analysis tool. To ameliorate this issue, we introduce a novel dynamic graph-based model which aims to forecast bookmaker odds for any match on any surface, allowing effective and detailed pre-tournament predictions to be made. By leveraging the high-quality information contained in the odds, our model can keep pace with new innovations in tennis modelling. By analysing major tennis championships from 2024 and 2025, we show that our model achieves comparable accuracy both to the bookmakers and other models in the literature, while significantly outperforming rankings-based predictions.

stat.AP↗

arXiv2025

Nonparametric Bounds for Evaluating the Clinical Utility of Treatment Rules

Evaluating the value of new clinical treatment rules based on patient characteristics is important but often complicated by hidden confounding factors in observational studies. Standard methods for estimating the average patient outcome if a new rule were universally adopted typically rely on strong, untestable assumptions about these hidden factors. This paper tackles this challenge by developing nonparametric bounds - a range of plausible values - for the expected outcome under a new rule, even with unobserved confounders present. We propose and investigate two main strategies for derivation of these bounds. We extend these techniques to incorporate Instrumental Variables (IVs), which can help narrow the bounds, and to directly estimate bounds on the difference in expected outcomes between the new rule and an existing clinical guideline. In simulation studies we compare the performance and width of bounds generated by the reduction and conditioning strategies in different scenarios. The methods are illustrated with a real-data example about prevention of peanut allergy in children. Our bounding frameworks provide robust tools for assessing the potential impact of new clinical treatment rules when unmeasured confounding is a concern.

stat.ME↗

arXiv2025

Phylo2Vec: a vector representation for binary trees

Binary phylogenetic trees inferred from biological data are central to understanding the shared history among evolutionary units. However, inferring the placement of latent nodes in a tree is computationally expensive. State-of-the-art methods rely on carefully designed heuristics for tree search, using different data structures for easy manipulation (e.g., classes in object-oriented programming languages) and readable representation of trees (e.g., Newick-format strings). Here, we present Phylo2Vec, a parsimonious encoding for phylogenetic trees that serves as a unified approach for both manipulating and representing phylogenetic trees. Phylo2Vec maps any binary tree with $n$ leaves to a unique integer vector of length $n-1$. The advantages of Phylo2Vec are fourfold: i) fast tree sampling, (ii) compressed tree representation compared to a Newick string, iii) quick and unambiguous verification if two binary trees are identical topologically, and iv) systematic ability to traverse tree space in very large or small jumps. As a proof of concept, we use Phylo2Vec for maximum likelihood inference on five real-world datasets and show that a simple hill-climbing-based optimisation scheme can efficiently traverse the vastness of tree space from a random to an optimal tree.

q-bio.PE↗

arXiv2025

Diffusion Models for Inverse Problems in the Exponential Family

Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due to the intractability of the likelihood score, which until now has only been approximated in the simpler case of Gaussian likelihoods. In this work, we extend diffusion models to handle inverse problems where the observations follow a distribution from the exponential family, such as a Poisson or a Binomial distribution. By leveraging the conjugacy properties of exponential family distributions, we introduce the evidence trick, a method that provides a tractable approximation to the likelihood score. In our experiments, we demonstrate that our methodology effectively performs Bayesian inference on spatially inhomogeneous Poisson processes with intensities as intricate as ImageNet images. Furthermore, we demonstrate the real-world impact of our methodology by showing that it performs competitively with the current state-of-the-art in predicting malaria prevalence estimates in Sub-Saharan Africa.

stat.ML↗

arXiv2025

Generalised Bayesian distance-based phylogenetics for the genomics era

As whole genomes become widely available, maximum likelihood and Bayesian phylogenetic methods are demonstrating their limits in meeting the escalating computational demands. Conversely, distance-based phylogenetic methods are efficient, but are rarely favoured due to their inferior performance. Here, we extend distance-based phylogenetics using an entropy-based likelihood of the evolution among pairs of taxa, allowing for fast Bayesian inference in genome-scale datasets. We provide evidence of a close link between the inference criteria used in distance methods and Felsenstein's likelihood, such that the methods are expected to have comparable performance in practice. Using the entropic likelihood, we perform Bayesian inference on three phylogenetic benchmark datasets and find that estimates closely correspond with previous inferences. We also apply this rapid inference approach to a 60-million-site alignment from 363 avian taxa, covering most avian families. The method has outstanding performance and reveals substantial uncertainty in the avian diversification events immediately after the K-Pg transition event. The entropic likelihood allows for efficient Bayesian phylogenetic inference, accommodating the analysis demands of the genomic era.

q-bio.PE↗

arXiv2024

Modelling the Stochastic Importation Dynamics and Establishment of Novel Pathogenic Strains using a General Branching Processes Framework

The importation and subsequent establishment of novel pathogenic strains in a population is subject to a large degree of uncertainty due to the stochastic nature of the disease dynamics. Mathematical models need to take this stochasticity in the early phase of an outbreak in order to adequately capture the uncertainty in disease forecasts. We propose a general branching process model of disease spread that includes host-level heterogeneity, and that can be straightforwardly tailored to capture the salient aspects of a particular disease outbreak. We combine this with a model of case importation that occurs via an independent marked Poisson process. We use this framework to investigate the impact of different control strategies, particularly on the time to establishment of an invading, exogenous strain, using parameters taken from the literature for COVID-19 as an example. We also demonstrate how to combine our model with a deterministic approximation, such that longer term projections can be generated that still incorporate the uncertainty from the early growth phase of the epidemic. Our approach produces meaningful short- and medium-term projections of the course of a disease outbreak when model parameters are still uncertain and when stochasticity still has a large effect on the population dynamics.

q-bio.PE↗

arXiv2024

KidSat: satellite imagery to map childhood poverty dataset and benchmark

Satellite imagery has emerged as an important tool to analyse demographic, health, and development indicators. While various deep learning models have been built for these tasks, each is specific to a particular problem, with few standard benchmarks available. We propose a new dataset pairing satellite imagery and high-quality survey data on child poverty to benchmark satellite feature representations. Our dataset consists of 33,608 images, each 10 km $\times$ 10 km, from 19 countries in Eastern and Southern Africa in the time period 1997-2022. As defined by UNICEF, multidimensional child poverty covers six dimensions and it can be calculated from the face-to-face Demographic and Health Surveys (DHS) Program . As part of the benchmark, we test spatial as well as temporal generalization, by testing on unseen locations, and on data after the training years. Using our dataset we benchmark multiple models, from low-level satellite imagery models such as MOSAIKS , to deep learning foundation models, which include both generic vision models such as Self-Distillation with no Labels (DINOv2) models and specific satellite imagery models such as SatMAE. We provide open source code for building the satellite dataset, obtaining ground truth data from DHS and running various models assessed in our work.

cs.CV↗

arXiv2024

Leaping through tree space: continuous phylogenetic inference for rooted and unrooted trees

Phylogenetics is now fundamental in life sciences, providing insights into the earliest branches of life and the origins and spread of epidemics. However, finding suitable phylogenies from the vast space of possible trees remains challenging. To address this problem, for the first time, we perform both tree exploration and inference in a continuous space where the computation of gradients is possible. This continuous relaxation allows for major leaps across tree space in both rooted and unrooted trees, and is less susceptible to convergence to local minima. Our approach outperforms the current best methods for inference on unrooted trees and, in simulation, accurately infers the tree and root in ultrametric cases. The approach is effective in cases of empirical data with negligible amounts of data, which we demonstrate on the phylogeny of jawed vertebrates. Indeed, only a few genes with an ultrametric signal were generally sufficient for resolving the major lineages of vertebrates. Optimisation is possible via automatic differentiation and our method presents an effective way forwards for exploring the most difficult, data-deficient phylogenetic questions.

q-bio.PE↗

arXiv2023

Continuous football player tracking from discrete broadcast data

Player tracking data remains out of reach for many professional football teams as their video feeds are not sufficiently high quality for computer vision technologies to be used. To help bridge this gap, we present a method that can estimate continuous full-pitch tracking data from discrete data made from broadcast footage. Such data could be collected by clubs or players at a similar cost to event data, which is widely available down to semi-professional level. We test our method using open-source tracking data, and include a version that can be applied to a large set of over 200 games with such discrete data.

cs.CV↗

arXiv2023

PriorCVAE: scalable MCMC parameter inference with Bayesian deep generative modelling

Recent advances have shown that GP priors, or their finite realisations, can be encoded using deep generative models such as variational autoencoders (VAEs). These learned generators can serve as drop-in replacements for the original priors during MCMC inference. While this approach enables efficient inference, it loses information about the hyperparameters of the original models, and consequently makes inference over hyperparameters impossible and the learned priors indistinct. To overcome this limitation, we condition the VAE on stochastic process hyperparameters. This allows the joint encoding of hyperparameters with GP realizations and their subsequent estimation during inference. Further, we demonstrate that our proposed method, PriorCVAE, is agnostic to the nature of the models which it approximates, and can be used, for instance, to encode solutions of ODEs. It provides a practical tool for approximate inference and shows potential in real-life spatial and spatiotemporal applications.

stat.ML↗

arXiv2023

Deep learning and MCMC with aggVAE for shifting administrative boundaries: mapping malaria prevalence in Kenya

Model-based disease mapping remains a fundamental policy-informing tool in the fields of public health and disease surveillance. Hierarchical Bayesian models have emerged as the state-of-the-art approach for disease mapping since they are able to both capture structure in the data and robustly characterise uncertainty. When working with areal data, e.g.~aggregates at the administrative unit level such as district or province, current models rely on the adjacency structure of areal units to account for spatial correlations and perform shrinkage. The goal of disease surveillance systems is to track disease outcomes over time. This task is especially challenging in crisis situations which often lead to redrawn administrative boundaries, meaning that data collected before and after the crisis are no longer directly comparable. Moreover, the adjacency-based approach ignores the continuous nature of spatial processes and cannot solve the change-of-support problem, i.e.~when estimates are required to be produced at different administrative levels or levels of aggregation. We present a novel, practical, and easy to implement solution to solve these problems relying on a methodology combining deep generative modelling and fully Bayesian inference: we build on the recently proposed PriorVAE method able to encode spatial priors over small areas with variational autoencoders by encoding aggregates over administrative units. We map malaria prevalence in Kenya, a country in which administrative boundaries changed in 2010.

cs.LG↗

arXiv2023

Intrinsic Randomness in Epidemic Modelling Beyond Statistical Uncertainty

Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever observe a single epidemic, and therefore cannot empirically determine aleatoric uncertainty. Here, we characterise both epistemic and aleatoric uncertainty using a time-varying general branching process. Our framework explicitly decomposes aleatoric variance into mechanistic components, quantifying the contribution to uncertainty produced by each factor in the epidemic process, and how these contributions vary over time. The aleatoric variance of an outbreak is itself a renewal equation where past variance affects future variance. We find that, superspreading is not necessary for substantial uncertainty, and profound variation in outbreak size can occur even without overdispersion in the offspring distribution (i.e. the distribution of the number of secondary infections an infected person produces). Aleatoric forecasting uncertainty grows dynamically and rapidly, and so forecasting using only epistemic uncertainty is a significant underestimate. Therefore, failure to account for aleatoric uncertainty will ensure that policymakers are misled about the substantially higher true extent of potential risk. We demonstrate our method, and the extent to which potential risk is underestimated, using two historical examples.

q-bio.PE↗

arXiv2023

A comparison of short-term probabilistic forecasts for the incidence of COVID-19 using mechanistic and statistical time series models

Short-term forecasts of infectious disease spread are a critical component in risk evaluation and public health decision making. While different models for short-term forecasting have been developed, open questions about their relative performance remain. Here, we compare short-term probabilistic forecasts of popular mechanistic models based on the renewal equation with forecasts of statistical time series models. Our empirical comparison is based on data of the daily incidence of COVID-19 across six large US states over the first pandemic year. We find that, on average, probabilistic forecasts from statistical time series models are overall at least as accurate as forecasts from mechanistic models. Moreover, statistical time series models better capture volatility. Our findings suggest that domain knowledge, which is integrated into mechanistic models by making assumptions about disease dynamics, does not improve short-term forecasts of disease incidence. We note, however, that forecasting is often only one of many objectives and thus mechanistic models remain important, for example, to model the impact of vaccines or the emergence of new variants.

stat.AP↗

arXiv2023

Seq2Seq Surrogates of Epidemic Models to Facilitate Bayesian Inference

Epidemic models are powerful tools in understanding infectious disease. However, as they increase in size and complexity, they can quickly become computationally intractable. Recent progress in modelling methodology has shown that surrogate models can be used to emulate complex epidemic models with a high-dimensional parameter space. We show that deep sequence-to-sequence (seq2seq) models can serve as accurate surrogates for complex epidemic models with sequence based model parameters, effectively replicating seasonal and long-term transmission dynamics. Once trained, our surrogate can predict scenarios a several thousand times faster than the original model, making them ideal for policy exploration. We demonstrate that replacing a traditional epidemic model with a learned simulator facilitates robust Bayesian inference.

cs.LG↗

arXiv2023

The interaction of transmission intensity, mortality, and the economy: a retrospective analysis of the COVID-19 pandemic

The COVID-19 pandemic has caused over 6.4 million registered deaths to date and has had a profound impact on economic activity. Here, we study the interaction of transmission, mortality, and the economy during the SARS-CoV-2 pandemic from January 2020 to December 2022 across 25 European countries. We adopt a Bayesian Mixed Effects model with auto-regressive terms. We find that increases in disease transmission intensity decreases Gross domestic product (GDP) and increases daily excess deaths, with a longer lasting impact on excess deaths in comparison to GDP, which recovers more rapidly. Broadly, our results reinforce the intuitive phenomenon that significant economic activity arises from diverse person-to-person interactions. We report on the effectiveness of non-pharmaceutical interventions (NPIs) on transmission intensity, excess deaths, and changes in GDP, and resulting implications for policy makers. Our results highlight a complex cost-benefit trade off from individual NPIs. For example, banning international travel increases GDP and reduces excess deaths. We consider country random effects and their associations with excess changes in GDP and excess deaths. For example, more developed countries in Europe typically had more cautious approaches to the COVID-19 pandemic, prioritising healthcare, and excess deaths over economic performance. Long term economic impairments are not fully captured by our model, as well as long term disease effects (Long Covid). Our results highlight that the impact of disease on a country is complex and multifaceted, and simple heuristic conclusions to extract the best outcome from the economy and disease burden are challenging.

stat.AP↗