Papers

Learning an optimal individualized treatment rule depends on reliable value comparisons across the candidate class. Standard doubly robust estimators are consistent when either the propensity score or outcome regression model is correctly specified, but they do not directly control the remaining bias in value estimation when both models are misspecified. In this paper, we propose a covariate balancing doubly robust estimator that combines propensity score estimation based on covariate balancing with an outcome regression component selected using an empirical variance criterion based on the influence function. Using prespecified covariate functions, the balancing procedure induces an effective balancing space to which the weighted propensity score error is orthogonal. Consequently, the proposed value estimator is consistent if either the propensity score model is correct or the rule-relevant outcome regression error lies in this space. The latter condition does not require a correctly specified outcome regression model and can hold even when both working models are misspecified. Under correct propensity score specification, the estimator has the smallest asymptotic variance within the proposed covariate balancing doubly robust class. Simulations evaluate value estimation in finite samples and the regret of learned rules, and an application to a leukemia dataset illustrates the proposed method in practice.

We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for solving maximum marginal likelihood estimation (MMLE) problems. Specifically, we provide a continuous-time framework for learning latent energy-based models, by defining stochastic differential equations (SDEs) that provably solve the MMLE problem. We obtain a practical algorithm as a discretisation of these SDEs and provide theoretical guarantees for the convergence of the proposed algorithm. Finally, we empirically validate the effectiveness of our method on synthetic and image datasets and demonstrate that using a particle based approach offers significant improvement in computational efficiency.

Meta-analysis can be formulated as combining $p$-values across studies into a joint $p$-value function, from which point estimates and confidence intervals can be derived. We extend the meta-analytic estimation framework based on combined $p$-value functions to incorporate uncertainty in heterogeneity estimation by employing a confidence distribution approach. Specifically, the confidence distribution of Edgington's method is adjusted according to the confidence distribution of the heterogeneity parameter constructed from the generalized heterogeneity statistic. Simulation results suggest that 95% confidence intervals approach nominal coverage under most scenarios involving more than three studies and heterogeneity. Under no heterogeneity or for only three studies, the confidence interval typically overcovers, but is often narrower than the Hartung-Knapp-Sidik-Jonkman interval. The point estimator exhibits small bias under model misspecification and moderate to large heterogeneity. Edgington's method provides a practical alternative to classical approaches, with adjustment for heterogeneity estimation uncertainty often improving confidence interval coverage.

This paper develops a nonparametric framework for identifying and estimating spatial boundaries of treatment effects in settings with geographic spillovers. While atmospheric dispersion theory predicts exponential decay of pollution under idealized assumptions, these assumptions – steady winds, homogeneous atmospheres, flat terrain – are systematically violated in practice. I establish nonparametric identification of spatial boundaries under weak smoothness and monotonicity conditions, propose a kernel-based estimator with data-driven bandwidth selection, and derive asymptotic theory for inference. Using 42 million satellite observations of NO$_2$ concentrations near coal plants (2019-2021), I find that nonparametric kernel regression reduces prediction errors by 1.0 percentage point on average compared to parametric exponential decay assumptions, with largest improvements at policy-relevant distances: 2.8 percentage points at 10 km (near-source impacts) and 3.7 percentage points at 100 km (long-range transport). Parametric methods systematically underestimate near-source concentrations while overestimating long-range decay. The COVID-19 pandemic provides a natural experiment validating the framework's temporal sensitivity: NO$_2$ concentrations dropped 4.6% in 2020, then recovered 5.7% in 2021. These results demonstrate that flexible, data-driven spatial methods substantially outperform restrictive parametric assumptions in environmental policy applications.

Accurate intraday forecasts are essential for power system operations, complementing day-ahead forecasts that gradually lose relevance as new information becomes available. This paper introduces a Bayesian updating mechanism that converts fully probabilistic day-ahead forecasts into intraday forecasts without retraining or re-inference. The approach conditions the Gaussian mixture output of a conditional variational autoencoder-based forecaster on observed measurements, yielding an updated distribution for the remaining horizon that preserves its probabilistic structure. This enables consistent point, quantile, and ensemble forecasts while remaining computationally efficient and suitable for real-time applications. Experiments on household electricity consumption and photovoltaic generation datasets demonstrate that the proposed method improves forecast accuracy up to 25% across likelihood-, sample-, quantile-, and point-based metrics. The largest gains occur in time steps with strong temporal correlation to observed data, and the use of pattern dictionary-based covariance structures further enhances performance. The results highlight a theoretically grounded framework for intraday forecasting in modern power systems.

Progress in AI is hindered by the lack of a programming language with all the requisite features. Libraries like PyTorch and TensorFlow provide automatic differentiation and efficient GPU implementation, but are additions to Python, which was never intended for AI. Their lack of support for automated reasoning and knowledge acquisition has led to a long and costly series of hacky attempts to tack them on. On the other hand, AI languages like LISP and Prolog lack scalability and support for learning. This paper proposes tensor logic, a language that solves these problems by unifying neural and symbolic AI at a fundamental level. The sole construct in tensor logic is the tensor equation, based on the observation that logical rules and Einstein summation are essentially the same operation, and all else can be reduced to them. I show how to elegantly implement key forms of neural, symbolic and statistical AI in tensor logic, including transformers, formal reasoning, kernel machines and graphical models. Most importantly, tensor logic makes new directions possible, such as sound reasoning in embedding space. This combines the scalability and learnability of neural networks with the reliability and transparency of symbolic reasoning, and is potentially a basis for the wider adoption of AI.

We develop a class of optimal tests for a structural break occurring at an unknown date in infinite and growing-order time series regression models, such as AR($\infty$), linear regression with increasingly many covariates, and nonparametric regression. Under an auxiliary i.i.d. Gaussian error assumption, we derive an average power optimal test, establishing a growing-dimensional analog of the exponential tests of Andrews and Ploberger (1994) to handle identification failure under the null hypothesis of no break. Relaxing the i.i.d. Gaussian assumption to a more general dependence structure, we establish a functional central limit theorem for the underlying stochastic processes, which features an extra high-order serial dependence term due to the growing dimension. We robustify our test both against this term and finite sample bias and illustrate its excellent performance and practical relevance in a Monte Carlo study and a real data empirical example.

We study the decoupled multi-armed bandit problem, where the learner separately selects one arm for exploration and one, possibly different, arm for exploitation at each round. In this setting, the loss of the explored arm is observed but not incurred, whereas the loss of the exploited arm is incurred without being observed. We propose an efficient Follow-the-Perturbed-Leader (FTPL) policy that achieves Best-of-Both-Worlds (BOBW) guarantee with constant regret in the stochastic regime and optimal $O(\sqrt{KT})$ regret in the adversarial regime. A key feature of our method is that it completely avoids both the convex optimization required by prior BOBW policies and the resampling procedures typically used in FTPL bandit policies. This allows FTPL to fully realize its computational efficiency advantages, leading to substantial reductions in computational cost. We empirically confirm that our policy not only improves the runtime but also demonstrates superior regret performance in both regimes.

We study neural network compressibility by using singular learning theory to extend the minimum description length (MDL) principle to singular models like neural networks. Through extensive experiments on the Pythia suite with quantization, factorization, and other compression techniques, we find that complexity estimates based on the local learning coefficient (LLC) are closely, and in some cases, linearly correlated with compressibility. Our results provide a path toward rigorously evaluating the limits of model compression.

Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are sensitive to outliers, which may lead to inaccurate parameter estimates and inferior classification accuracy. We propose a robust estimation procedure for functional logistic regression, in which the observations of the functional predictor are projected onto a set of finite-dimensional subspaces via robust functional principal component analysis. This dimension-reduction step reduces the outlying effects in the functional predictor. The logistic regression coefficient is estimated using an M-type estimator based on binary response and robust principal component scores. In doing so, we provide robust estimates by minimizing the effects of outliers in the binary response and functional predictor variables. Via a series of Monte-Carlo simulations and using hand radiograph data, we examine the parameter estimation and classification accuracy for the response variable. We find that the robust procedure outperforms some existing robust and non-robust methods when outliers are present, while producing competitive results when outliers are absent. In addition, the proposed method is computationally more efficient than some existing robust alternatives.

Mamba, a recently proposed linear-time sequence model, has attracted significant attention for its computational efficiency and strong empirical performance. However, a rigorous theoretical understanding of its underlying mechanisms remains limited. In this work, we provide a theoretical analysis of Mamba's in-context learning (ICL) capability by focusing on tasks defined by low-dimensional nonlinear target functions. Specifically, we study in-context learning of a single-index model $y \approx g_*(\langle \boldsymbol{\beta}, \boldsymbol{x} \rangle)$, which depends on only a single relevant direction $\boldsymbol{\beta}$, referred to as feature. We prove that Mamba, pretrained by gradient-based methods, can achieve efficient ICL via test-time feature learning, extracting the relevant direction directly from context examples. Consequently, we establish a test-time sample complexity that improves upon linear Transformers – analyzed to behave like kernel methods – and is comparable to nonlinear Transformers, which have been shown to surpass the Correlational Statistical Query (CSQ) lower bound and achieve near information-theoretically optimal rate in previous works. Our analysis reveals the crucial role of the nonlinear gating mechanism in Mamba for feature extraction, highlighting it as the fundamental driver behind Mamba's ability to achieve both computational efficiency and high performance.

We propose DeepMartingale, a deep-learning framework for the dual formulation of discrete-monitoring optimal stopping problems under continuous-time models. Leveraging a martingale representation, our method implements a pure-dual procedure that directly optimizes over a parameterized class of martingales, producing computable and tight dual upper bounds for the value function in high-dimensional settings without requiring any primal information or Snell-envelope approximation. We prove convergence of the resulting upper bounds under mild assumptions for both first- and second-moment losses. A key contribution is an expressivity theorem showing that DeepMartingale can approximate the true value function to any prescribed accuracy $\varepsilon$ using neural networks of size at most $\tilde{c} d^{\tilde{q}}\varepsilon^{-\tilde{r}}$, with constants independent of the dimension $d$ and accuracy $\varepsilon$, thereby avoiding the curse of dimensionality. Since expressivity in this setting translates into scalability, our theory also motivates estimating the dimension scaling law to guide architecture design and the training setup in deep learning-based numerical computation and the choice of rebalancing frequency for the related hedging strategy. The learned martingale representation further yields a practical and dimension-scalable deep delta hedging strategy. Numerical experiments on high-dimensional Bermudan option benchmarks confirm convergence, expressivity, scalable training, and the stability of the resulting upper bounds and hedging performance.

We introduce a Markov Chain Monte Carlo (MCMC) algorithm that dramatically accelerates the simulation of quantum many-body systems, a grand challenge in computational science. State-of-the-art methods for these problems are severely limited by $O(N^3)$ computational complexity. Our method avoids this bottleneck, achieving near-linear $O(N \log N)$ scaling per sweep. Our approach samples a joint probability measure over two coupled variable sets: (1) particle trajectories of the fundamental fermions, and (2) auxiliary variables that decouple fermion interactions. The key innovation is a novel transition kernel for particle trajectories formulated in the Fourier domain, revealing the transition probability as a convolution that enables massive acceleration via the Fast Fourier Transform (FFT). The auxiliary variables admit closed-form, factorized conditional distributions, enabling efficient exact Gibbs sampling update. We validate our algorithm on benchmark quantum physics problems, accurately reproducing known theoretical results and matching traditional $O(N^3)$ algorithms on $32\times 32$ lattice simulations at a fraction of the wall-clock time, empirically demonstrating $N \log N$ scaling. By reformulating a long-standing physics simulation problem in machine learning language, our work provides a powerful tool for large-scale probabilistic inference and opens avenues for physics-inspired generative models.

Stochastic Gradient Descent (SGD) and its Ruppert-Polyak averaged variant (ASGD) lie at the heart of modern large-scale learning, yet their theoretical properties in high-dimensional settings are rarely understood. In this paper, we provide rigorous statistical guarantees for constant learning-rate SGD and ASGD in high-dimensional regimes. Our key innovation is to transfer powerful tools from high-dimensional time series to online learning. Specifically, by viewing SGD as a nonlinear autoregressive process and adapting existing coupling techniques, we prove the geometric-moment contraction of high-dimensional SGD for constant learning rates, thereby establishing asymptotic stationarity of the iterates. Building on this, we derive the $q$-th moment convergence of SGD and ASGD for any $q\ge2$ in general $\ell^s$-norms, and, in particular, the $\ell^{\infty}$-norm that is frequently adopted in high-dimensional sparse or structured models. Furthermore, we provide sharp high-probability concentration analysis which entails the probabilistic bound of high-dimensional ASGD. Beyond closing a critical gap in SGD theory, our proposed framework offers a novel toolkit for analyzing a broad class of high-dimensional learning algorithms.

Reconstructing evolutionary histories and estimating the rate of evolution from molecular sequence data is of central importance in evolutionary biology and infectious disease research. We introduce a flexible Bayesian phylogenetic inference framework that accommodates changing evolutionary rates over time by modeling sequence character substitution processes as inhomogeneous continuous-time Markov chains (ICTMCs) acting along the unknown phylogeny, where the rate remains as an unknown, positive and integrable function of time. The integral of the rate function appears in the finite-time transition probabilities of the ICTMCs that must be efficiently computed for all branches of the phylogeny to evaluate the observed data likelihood. Circumventing computational challenges that arise from a fully nonparametric function, we successfully parameterize the rate function as piecewise constant with a large number of epochs that we call the polyepoch clock model. This makes the transition probability computation relatively inexpensive and continues to flexibly capture rate change over time. We employ a Gaussian Markov random field prior to achieve temporal smoothing of the estimated rate function. Hamiltonian Monte Carlo sampling enabled by scalable gradient evaluation under this model makes our framework computationally efficient. We assess the performance of the polyepoch clock model in recovering the true timescales and rates through simulations under two different evolutionary scenarios. We then apply the polyepoch clock model to examine the rates of West Nile virus, Dengue virus and influenza A/H3N2 evolution, and estimate the time-varying rate of SARS-CoV-2 spread in Europe in 2020.

Extreme value theory (EVT) is well suited to model extreme events, such as floods, heatwaves, or mechanical failures, which is required for reliability assessment of systems across multiple domains for risk management and loss prevention. The block maxima (BM) method, a particular approach within EVT, starts by dividing the historical observations into blocks. Then the sample of the maxima for each block can be shown, under some assumptions, to converge to a known class of distributions, which can then be used for analysis. The question of automatic (i.e., without explicit expert input) selection of the block size remains an open challenge. This work proposes a novel Bayesian framework, namely, multi-objective Bayesian optimization (MOBO-D*), to optimize BM blocking for accurate modeling and prediction of extremes in EVT. MOBO-D* formulates two objectives: goodness-of-fit of the distribution of extreme events and the accurate prediction of extreme events to construct an estimated Pareto front for optimal blocking choices. The efficacy of the proposed framework is illustrated by applying it to a real-world case study from the domain of additive manufacturing as well as a synthetic dataset. MOBO-D* outperforms a number of benchmarks and can be naturally extended to high-dimensional cases. The computational experiments show that it can be a promising approach in applications that require repeated automated block size selection, such as optimization or analysis of many datasets at once.

Characterizing interactions between brain areas is a fundamental goal of systems neuroscience. While such analyses are possible when areas are recorded simultaneously, it is rare to observe all combinations of areas of interest within a single animal or recording session. How can we leverage multi-animal datasets to better understand multi-area interactions? Building on recent progress in large-scale, multi-animal models, we introduce NeuroPaint, a masked autoencoding approach for inferring the dynamics of unrecorded brain areas. By training across animals with overlapping subsets of recorded areas, NeuroPaint learns to reconstruct activity in missing areas based on shared structure across individuals. We train and evaluate our approach on synthetic data and two multi-animal, multi-area Neuropixels datasets. Our results demonstrate that models trained across animals with partial observations can successfully in-paint the dynamics of unrecorded areas, enabling multi-area analyses that transcend the limitations of any single experiment.

Diffusion-based samplers learn to sample complex, high-dimensional distributions using energies or log densities alone, without training data. Yet, they remain impractical for molecular sampling because they are often slower than molecular dynamics and miss thermodynamically relevant modes. Inspired by enhanced sampling, we encourage exploration by introducing a sequential bias along bespoke, information-rich, low-dimensional projections of atomic coordinates known as collective variables (CVs). We introduce a repulsive potential centered on the CVs from recent samples, which pushes future samples towards novel CV regions and effectively increases the temperature in the projected space. Our resulting method improves efficiency, mode discovery, enables the estimation of free energy differences, and retains independent sampling from the approximate Boltzmann distribution via reweighting by the bias. On standard peptide conformational sampling benchmarks, the method recovers diverse conformational states and accurate free energy profiles. We are the first to demonstrate reactive sampling using a diffusion-based sampler, capturing bond breaking and formation with universal interatomic potentials at near-first-principles accuracy. The approach resolves reactive energy landscapes at a fraction of the wall-clock time of standard sampling methods, advancing diffusion-based sampling towards practical use in molecular sciences.

We propose a new general framework for recovering low-rank structure in optimal transport using Schatten-$p$ norm regularization. Our approach extends existing methods that promote sparse and interpretable transport maps or plans, while providing a unified and principled family of convex programs that encourage low-dimensional structure. The convexity of our formulation enables direct theoretical analysis: we derive optimality conditions and prove recovery guarantees for low-rank couplings and barycentric maps in simplified settings. To efficiently solve the proposed program, we develop a mirror descent algorithm with convergence guarantees for $p \geq 1$. Experiments on synthetic and real data demonstrate the method's efficiency, scalability, and ability to recover low-rank transport structures.

Robust reinforcement learning (Robust RL) seeks to handle epistemic uncertainty in environment dynamics, but existing approaches often rely on nested min–max optimization, which is computationally expensive and yields overly conservative policies. We propose Adaptive Rank Representation (AdaRL), a bi-level optimization framework that improves robustness by aligning policy complexity with the intrinsic dimension of the task. At the lower level, AdaRL performs policy optimization under fixed-rank constraints with dynamics sampled from a Wasserstein ball around a centroid model. At the upper level, it adaptively adjusts the rank to balance the bias–variance trade-off, projecting policy parameters onto a low-rank manifold. This design avoids solving adversarial worst-case dynamics while ensuring robustness without over-parameterization. Empirical results on MuJoCo continuous control benchmarks demonstrate that AdaRL not only consistently outperforms fixed-rank baselines (e.g., SAC) and state-of-the-art robust RL methods (e.g., RNAC, Parseval), but also converges toward the intrinsic rank of the underlying tasks. These results highlight that adaptive low-rank policy representations provide an efficient and principled alternative for robust RL under model uncertainty.

We study statistical estimation under local differential privacy (LDP) when users may hold heterogeneous privacy levels and accuracy must be guaranteed with high probability. Departing from the common in-expectation analyses, and for one-dimensional and multi-dimensional mean estimation problems, we develop finite sample upper bounds in $\ell_2$-norm that hold with probability at least $1-\beta$. We complement these results with matching minimax lower bounds, establishing the optimality (up to constants) of our guarantees in the heterogeneous LDP regime. We further study distribution learning in $\ell_\infty$-distance, designing an algorithm with high-probability guarantees under heterogeneous privacy demands. Our techniques offer principled guidance for designing mechanisms in settings with user-specific privacy levels.

Active subspace analysis uses the leading eigenspace of the gradient's second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator which coincides with the active subspace matrix when applied to a Euclidean space. We show that many of the desirable properties of Active Subspace analysis extend directly to the infinite dimensional setting. We also propose a Monte Carlo procedure and discuss its convergence properties. Finally, we deploy this methodology to create visualizations and improve modeling and optimization on complex test problems.

In many causal inference problems, multiple action variables share a common causal role yet lack a natural ordering. \revblue{We consider $K\geq2$ action variables, each evaluated under treatment or control conditions,} and formalize permutation equivariance, the principle that permuting the variables permutes the corresponding estimands in a trackable manner, hence preserving their scientific meaning. We characterize this principle algebraically and present a complete class of weighted permutation equivariant estimands capturing main effects and interactions of all orders. We discuss the interpretation and choice of weights and characterize residual-free estimands, whose inclusion–exclusion sum recovers the endpoint contrast between the all-treated and all-control configurations. \revblue{Applying our general framework to network interference yields a new hierarchy of direct, indirect, and overall effects, whose first-order aggregates recover the average effects of \citet{hu2022average}. We also identify the overall effects as mixed derivatives of expected welfare under independent Bernoulli assignment.} We illustrate the framework through the contexts of factorial studies, causal mediation, and network interference.

The Maximum Mean Discrepancy (MMD) is a widely used multivariate distance metric for two-sample testing. The standard MMD test statistic has an intractable null distribution typically requiring costly resampling or permutation approaches for calibration. In this work we leverage a martingale interpretation of the estimated squared MMD to propose martingale MMD (mMMD), a quadratic-time statistic which has a limiting standard Gaussian distribution under the null. Moreover we show that the test is consistent against any fixed alternative and for large sample sizes, mMMD offers substantial computational savings over the standard MMD test, with only a minor loss in power.

Contrastive dimension reduction (CDR) methods aim to extract signal unique to or enriched in a treatment (foreground) group relative to a control (background) group. This setting arises in many scientific domains, such as genomics, imaging, and time series analysis, where traditional dimension reduction techniques such as Principal Component Analysis (PCA) may fail to isolate the signal of interest. In this review, we provide a systematic overview of existing CDR methods. We propose a pipeline for analyzing case-control studies together with a taxonomy of CDR methods based on their assumptions, objectives, and mathematical formulations, unifying disparate approaches under a shared conceptual framework. We highlight key applications and challenges in existing CDR methods, and identify open questions and future directions. By providing a clear framework for CDR and its applications, we aim to facilitate broader adoption and motivate further developments in this emerging field.

Random geometric graphs (RGGs) offer a powerful tool for analyzing the geometric and dependence structures in real-world networks. For example, it has been observed that RGGs are a good model for protein-protein interaction networks. In RGGs, nodes are randomly distributed over an $m$-dimensional metric space, and edges connect the nodes if and only if their distance is less than some threshold. When fitting RGGs to real-world networks, the first step is probably to input or estimate the dimension $m$. However, it is not clear whether the prespecified dimension is equal to the true dimension. In this paper, we investigate this problem using hypothesis testing. Under the null hypothesis, the dimension is equal to a specific value, while the alternative hypothesis asserts the dimension is not equal to that value. We propose the first statistical test. Under the null hypothesis, the proposed test statistic converges in law to the standard normal distribution, and under the alternative hypothesis, the test statistic is unbounded in probability. We derive the asymptotic distribution by leveraging the asymptotic theory of degenerate U-statistics with kernel function dependent on the number of nodes. This approach differs significantly from prevailing methods used in network hypothesis testing problems. Moreover, we also propose an efficient approach to compute the test statistic based on the adjacency matrix. Simulation studies show that the proposed test performs well. We also apply the proposed test to multiple real-world networks to test their dimensions.

In Bayesian Optimization (BO), additive assumptions can mitigate the twin difficulties of modeling and searching a complex function in high dimension. However, common acquisition functions, like the Additive Lower Confidence Bound, ignore pairwise covariances between dimensions, which we'll call bilateral uncertainty (BU), imposing a second layer of approximations. While theoretical results indicate that asymptotically not much is lost in doing so, little is known about the practical effects of this assumption in small budgets. In this article, we show that by exploiting conditional independence, Thompson Sampling respecting BU can be efficiently conducted. We use this fact to execute an empirical investigation into the loss incurred by ignoring BU, finding that the additive approximation to Thompson Sampling does indeed have, on balance, worse performance than the exact method, but that this difference is of little practical significance. This buttresses the theoretical understanding and suggests that the BU-ignoring approximation is sufficient for BO in practice, even in the non-asymptotic regime.

We study the convergence rate of learning pairwise interactions in single-layer attention-style models, where tokens interact through a weight matrix and a nonlinear activation function. We prove that the minimax rate is $M^{-\frac{2\beta}{2\beta+1}}$, where $M$ is the sample size and $\beta$ is the Hölder smoothness of the activation function. Importantly, this rate is independent of the embedding dimension $d$, the number of tokens $N$, and the rank $r$ of the weight matrix, provided that $rd \le (M/\log M)^{\frac{1}{2\beta+1}}$. These results highlight a fundamental statistical efficiency of attention-style models, even when the weight matrix and activation are not separately identifiable, and provide a theoretical understanding of attention mechanisms and guidance on training.

This paper proposes a synergy of amortised and particle-based methods for sampling from distributions defined by unnormalised density functions. We state a connection between sequential Monte Carlo (SMC) and neural sequential samplers trained by maximum-entropy reinforcement learning (MaxEnt RL), wherein learnt sampling policies and value functions define proposal kernels and twist functions. Exploiting this connection, we introduce an off-policy RL training procedure for the sampler that uses samples from SMC – using the learnt sampler as a proposal – as a behaviour policy that better explores the target distribution. We describe techniques for stable joint training of proposals and twist functions and an adaptive weight tempering scheme to reduce training signal variance. Furthermore, building upon past attempts to use experience replay to guide the training of neural samplers, we derive a way to combine historical samples with annealed importance sampling weights within a replay buffer. On synthetic multi-modal targets (in both continuous and discrete spaces) and the Boltzmann distribution of alanine dipeptide conformations, we demonstrate improvements in approximating the true distribution as well as training stability compared to both amortised and Monte Carlo methods.

Many scientific analyses require simultaneous comparison of multiple functionals of an unknown signal at once, calling for multidimensional confidence regions with guaranteed simultaneous frequentist under structural constraints (e.g., non-negativity, shape, or physics-based). This paper unifies and extends many previous optimization-based approaches to constrained confidence region construction in linear inverse problems through the lens of statistical test inversion. We begin by reviewing the historical development of optimization-based confidence intervals for the single-functional setting, from "strict bounds" to the Burrus conjecture and its recent refutation via the aforementioned test inversion framework. We then extend this framework to the multiple-functional setting. This framework can be used to: (i) improve the calibration constants of previous methods, yielding smaller confidence regions that still preserve frequentist coverage, (ii) obtain tractable multidimensional confidence regions that need not be hyper-rectangles to better capture functional dependence structure, and (iii) generalize beyond Gaussian error distributions to generic log-concave error distributions. We provide theory establishing nominal simultaneous coverage of our methods and show quantitative volume improvements relative to prior approaches using numerical experiments.