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Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI methods have made use of neural networks (NN) to provide approximate, yet expressive constructs for the unavailable likelihood function and the posterior distribution. However, they do not generally achieve an optimal trade-off between accuracy and computational demand. In this work, we propose an alternative that provides both approximations to the likelihood and the posterior distribution, using structured mixtures of probability distributions. Our approach produces accurate posterior inference when compared to state-of-the-art NN-based SBI methods, while exhibiting a much smaller computational footprint. We illustrate our results on several benchmark models from the SBI literature.

We establish a near-optimality guarantee for the full orthogonalization method (FOM), showing that the overall convergence of FOM is nearly as good as GMRES. In particular, we prove that at every iteration $k$, there exists an iteration $j\leq k$ for which the FOM residual norm at iteration $j$ is no more than $\sqrt{k+1}$ times larger than the GMRES residual norm at iteration $k$. This bound is sharp, and it has implications for algorithms for approximating the action of a matrix function on a vector.

Maximum entropy (Maxent) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, Maxent models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for Maxent models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical Maxent models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth Maxent models. Our proposed first-order algorithms leverage the Kullback-Leibler divergence to train large-scale and non-smooth Maxent models efficiently. For Maxent models with discrete probability distribution of $n$ elements built from samples, each containing $m$ features, the stepsize parameters estimation and iterations in our algorithms scale on the order of $O(mn)$ operations and can be trivially parallelized. Moreover, the strong $\ell_{1}$ convexity of the Kullback--Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the arts by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

First-order methods are often analyzed via their continuous-time models, where their worst-case convergence properties are usually approached via Lyapunov functions. In this work, we provide a systematic and principled approach to find and verify Lyapunov functions for classes of ordinary and stochastic differential equations. More precisely, we extend the performance estimation framework, originally proposed by Drori and Teboulle [10], to continuous-time models. We retrieve convergence results comparable to those of discrete methods using fewer assumptions and convexity inequalities, and provide new results for stochastic accelerated gradient flows.

Charts, figures, and text derived from data play an important role in decision making, from data-driven policy development to day-to-day choices informed by online articles. Making sense of, or fact-checking, outputs means understanding how they relate to the underlying data. Even for domain experts with access to the source code and data sets, this poses a significant challenge. In this paper we introduce a new program analysis framework which supports interactive exploration of fine-grained I/O relationships directly through computed outputs, making use of dynamic dependence graphs. Our main contribution is a novel notion in data provenance which we call related inputs, a relation of mutual relevance or "cognacy" which arises between inputs when they contribute to common features of the output. Queries of this form allow readers to ask questions like "What outputs use this data element, and what other data elements are used along with it?". We show how Jonsson and Tarski's concept of conjugate operators on Boolean algebras appropriately characterises the notion of cognacy in a dependence graph, and give a procedure for computing related inputs over such a graph.

We present a data-driven control architecture for modifying the kinematics of robots and artificial avatars to encode specific information such as the presence or not of an emotion in the movements of an avatar or robot driven by a human operator. We validate our approach on an experimental dataset obtained during the reach-to-grasp phase of a pick-and-place task.

The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong to the class of mixtures on which the estimator is based. In a situation where $P$ is a mixture of well enough separated but nonparametric distributions it is shown that the components of the population version of the estimator correspond to the well separated components of $P$. This provides some theoretical justification for the use of such estimators for cluster analysis in case that $P$ has well separated subpopulations even if these subpopulations differ from what the mixture model assumes.

This article is concerned with the multilevel Monte Carlo (MLMC) methods for approximating expectations of some functions of the solution to the Heston 3/2-model from mathematical finance, which takes values in $(0, \infty)$ and possesses superlinearly growing drift and diffusion coefficients. To discretize the SDE model, a new Milstein-type scheme is proposed to produce independent sample paths. The proposed scheme can be explicitly solved and is positivity-preserving unconditionally, i.e., for any time step-size $h>0$. This positivity-preserving property for large discretization time steps is particularly desirable in the MLMC setting. Furthermore, a mean-square convergence rate of order one is proved in the non-globally Lipschitz regime, which is not trivial, as the diffusion coefficient grows super-linearly. The obtained order-one convergence in turn promises the desired relevant variance of the multilevel estimator and justifies the optimal complexity $\mathcal{O}(\epsilon^{-2})$ for the MLMC approach, where $\epsilon > 0$ is the required target accuracy. Numerical experiments are finally reported to confirm the theoretical findings.

Mendelian randomization is an instrumental variable method that utilizes genetic information to investigate the causal effect of a modifiable exposure on an outcome. In most cases, the exposure changes over time. Understanding the time-varying causal effect of the exposure can yield detailed insights into mechanistic effects and the potential impact of public health interventions. Recently, a growing number of Mendelian randomization studies have attempted to explore time-varying causal effects. However, the proposed approaches oversimplify temporal information and rely on overly restrictive structural assumptions, limiting their reliability in addressing time-varying causal problems. This paper considers a novel approach to estimate time-varying effects through continuous-time modelling by combining functional principal component analysis and weak-instrument-robust techniques. Our method effectively utilizes available data without making strong structural assumptions and can be applied in general settings where the exposure measurements occur at different timepoints for different individuals. We demonstrate through simulations that our proposed method performs well in estimating time-varying effects and provides reliable inference results when the time-varying effect form is correctly specified. The method could theoretically be used to estimate arbitrarily complex time-varying effects. However, there is a trade-off between model complexity and instrument strength. Estimating complex time-varying effects requires instruments that are unrealistically strong. We illustrate the application of this method in a case study examining the time-varying effects of systolic blood pressure on urea levels.

Temporal network data is often encoded as time-stamped interaction events between senders and receivers, such as co-authoring scientific articles or communication via email. A number of relational event frameworks have been proposed to address specific issues raised by complex temporal dependencies. These models attempt to quantify how individual behaviour, endogenous and exogenous factors, as well as interactions with other individuals modify the network dynamics over time. It is often of interest to determine whether changes in the network can be attributed to endogenous mechanisms reflecting natural relational tendencies, such as reciprocity or triadic effects. The propensity to form or receive ties can also, at least partially, be related to actor attributes. Nodal heterogeneity in the network is often modelled by including actor-specific or dyadic covariates. However, comprehensively capturing all personality traits is difficult in practice, if not impossible. A failure to account for heterogeneity may confound the substantive effect of key variables of interest. This work shows that failing to account for node level sender and receiver effects can induce ghost triadic effects. We propose a random-effect extension of the relational event model to deal with these problems. We show that it is often effective over more traditional approaches, such as in-degree and out-degree statistics. These results that the violation of the hierarchy principle due to insufficient information about nodal heterogeneity can be resolved by including random effects in the relational event model as a standard.