arXiv subjects

Filippo Monti

Publications and source records attributed to Filippo Monti.

4 recordsLinked to original sources

arXiv2026

BEAGLE in Action: Phylogenetic Likelihoods for Very Large State Spaces

Computing phylogenetic likelihoods becomes challenging when the continuous-time Markov chain has a large state space. At each branch, pruning algorithms require terms of the form $e^{Q t}\cdot B$, where $Q$ is an $S \times S$ rate matrix (e.g., for $S$ states), $t$ is a branch length, and the columns of matrix $B$ (e.g., $B \in \mathbb{R}_{+}^{S \times L}$) are partial-likelihood vectors for $L$ site patterns. Many implementations calculate the dense transition matrix $P(t)=e^{Q t}$ via eigendecomposition and multiply it by $B$. This strategy is efficient for small state spaces, but it can be inefficient for large sparse rate matrices because forming $P(t)$ or its eigen vector matrices destroys sparsity and its cost may not be well amortized when $L$ is small. We implement an alternative likelihood kernel based on the Al-Mohy and Higham (2011) algorithm for computing the action of the matrix exponential directly, avoiding explicit construction of $P(t)$ or its eigen vector matrices. The resulting method takes full advantage of the sparsity of $Q$. We implement this method as a CPU-based extension to the BEAGLE library and evaluate it on two large-state molecular models: a Markov-modulated codon model of heterotachy with $M$ selective regimes and $61\cdot M$ possible states, and a codon-pair model of interlocus gene conversion between two paralogs with $61^2=3\,721$ possible states. Our results characterize when action-based likelihood computation improves performance over calculating $e^{Q t}$ directly. We show that this method enables fast, scalable inference for complex models, removing a key computational barrier to the study of evolution with large state space models.

stat.CO↗

arXiv2026

Stable Matrix Parametrizations and Structured Adjoints for Ornstein-Uhlenbeck Processes

Ornstein-Uhlenbeck processes with flexible multivariate drift matrices are powerful models for capturing coupled, asymmetric, and damped-oscillatory mean reversion. However, likelihood-based inference is challenging because the drift matrix must remain Hurwitz stable, while likelihood and gradient evaluations require repeated, costly computation and differentiation of the drift matrix exponential and of solutions to the associated Lyapunov equation. We introduce the Hurwitz smooth spectral block parametrization (H-SSBP), which represents the drift as a change of basis applied to independent one- and two-dimensional stable blocks. Simple scalar constraints enforce Hurwitz stability, while the two-dimensional blocks vary smoothly between real- and complex-eigenvalue regimes, avoiding discrete model selection. The H-SSBP represents every real Hurwitz matrix diagonalizable over the complex numbers and has dense, full-measure support within the Hurwitz cone. Its block structure reduces the OU transition matrix, stationary and innovation covariances, and their reverse-mode derivatives to constant-size block or block-pair computations plus change-of-basis multiplications. Numerical experiments demonstrate dramatic speed-ups over alternatives, particularly for matrix-exponential adjoints and Lyapunov-equation kernels. Real-data analyses of asynchronous financial data and multivariate phylogenetic traits illustrate the proposed framework in practice.

stat.CO↗

arXiv2026

Nonparametric Modeling of Continuous-Time Markov Chains

Inferring the infinitesimal rates of continuous-time Markov chains (CTMCs) is a central challenge in many scientific domains. This task is difficult because the number of rates grows quadratically with the state space, rates can be strongly dependent, and many transitions may be only partially observed. We introduce a Bayesian framework that models CTMC rates as flexible functions of covariates through Gaussian processes. This enables nonlinear covariate effects, improves inference by incorporating external information, and helps identify potential drivers of CTMC dynamics. For posterior inference, we use Hamiltonian Monte Carlo and develop scalable exact and approximate gradients for likelihoods involving repeated matrix exponentials. With $N$ observations and $K$ CTMC states, these gradients reduce the dominant cost of existing derivative calculations from $O(NK^3)$, with large constants, to $O(K^3+NK^2)$, with cheaper constants. We demonstrate the method in Bayesian phylogenetic and phylogeographic inference, where CTMCs are central, and show strong performance on synthetic and real datasets, including empirical quadratic scaling in $K$ even when $N<K$.

stat.ME↗

arXiv2026

Non-Linear Drivers of Population Dynamics: a Nonparametric Coalescent Approach

Effective population size (Ne(t)) is a fundamental parameter in population genetics and phylodynamics that quantifies genetic diversity and reveals demographic history. Coalescent-based methods enable the inference of Ne(t) trajectories through time from phylogenies reconstructed from molecular sequence data. Understanding the ecological and environmental drivers of population dynamics requires linking Ne(t) to external covariates. Existing approaches typically impose log-linear relationships between covariates and Ne(t), which may fail to capture complex biological processes and can introduce bias when the true relationship is nonlinear. We present a flexible Bayesian framework that integrates covariates into coalescent models with piecewise-constant Ne(t) through a Gaussian process (GP) prior. The GP, a distribution over functions, naturally accommodates nonlinear covariate effects without restrictive parametric assumptions. This formulation improves estimation of covariate-Ne(t) relationships, mitigates bias under nonlinear associations, and yields interpretable uncertainty quantification that varies across the covariate space. To balance global covariate-driven patterns with local temporal dynamics, we couple the GP prior with a Gaussian Markov random field that enforces smoothness in Ne(t) trajectories. Through simulation studies and three empirical applications - yellow fever virus dynamics in Brazil (2016-2018), late-Quaternary musk ox demography, and HIV-1 CRF02-AG evolution in Cameroon - we demonstrate that our method both confirms linear relationships where appropriate and reveals nonlinear covariate effects that would otherwise be missed or mischaracterized. This framework advances phylodynamic inference by enabling more accurate and biologically realistic modeling of how environmental and epidemiological factors shape population size through time.

stat.AP↗