We investigate how to select the number of communities for weighted networks without a full likelihood modeling. First, we propose a novel weighted degree-corrected stochastic block model (DCSBM), in which the mean adjacency matrix is modeled as the same as in standard DCSBM, while the variance profile matrix is assumed to be related to the mean adjacency matrix through a given variance function. Our method of selection the number of communities is based on a sequential testing framework, in each step the weighed DCSBM is fitted via some spectral clustering method. A key step is to carry out matrix scaling on the estimated variance profile matrix. The resulting scaling factors can be used to normalize the adjacency matrix, from which the testing statistic is obtained. Under mild conditions on the weighted DCSBM, our proposed procedure is shown to be consistent in estimating the true number of communities. Numerical experiments on both simulated and real network data also demonstrate the desirable empirical properties of our method.

A common objective in the analysis of tabular data is estimating the conditional distribution (in contrast to only producing predictions) of a set of "outcome" variables given a set of "covariates", which is sometimes referred to as the "density regression" problem. Beyond estimation on the conditional distribution, the generative ability of drawing synthetic samples from the learned conditional distribution is also desired as it further widens the range of applications. We propose a flow-based generative model tailored for the density regression task on tabular data. Our flow applies a sequence of tree-based piecewise-linear transforms on initial uniform noise to eventually generate samples from complex conditional densities of (univariate or multivariate) outcomes given the covariates and allows efficient analytical evaluation of the fitted conditional density on any point in the sample space. We introduce a training algorithm for fitting the tree-based transforms using a divide-and-conquer strategy that transforms maximum likelihood training of the tree-flow into training a collection of binary classifiers--one at each tree split--under cross-entropy loss. We assess the performance of our method under out-of-sample likelihood evaluation and compare it with a variety of state-of-the-art conditional density learners on a range of simulated and real benchmark tabular datasets. Our method consistently achieves comparable or superior performance at a fraction of the training and sampling budget. Finally, we demonstrate the utility of our method's generative ability through an application to generating synthetic longitudinal microbiome compositional data based on training our flow on a publicly available microbiome study.

The limitations of purely neural learning have sparked an interest in probabilistic neurosymbolic models, which combine neural networks with probabilistic logical reasoning. As these neurosymbolic models are trained with gradient descent, we study the complexity of differentiating probabilistic reasoning. We prove that although approximating these gradients is intractable in general, it becomes tractable during training. Furthermore, we introduce WeightME, an unbiased gradient estimator based on model sampling. Under mild assumptions, WeightME approximates the gradient with probabilistic guarantees using a logarithmic number of calls to a SAT solver. Lastly, we evaluate the necessity of these guarantees on the gradient. Our experiments indicate that the existing biased approximations indeed struggle to optimize even when exact solving is still feasible.

Random effects meta-analysis model is an important tool for integrating results from multiple independent studies. However, the standard model is based on the assumption of normal distributions for both random effects and within-study errors, making it susceptible to outlying studies. Although robust modeling using the $t$ distribution is an appealing idea, the existing work, that explores the use of the $t$ distribution only for random effects, involves complicated numerical integration and numerical optimization. In this paper, a novel robust meta-analysis model using the $t$ distribution is proposed ($t$Meta). The novelty is that the marginal distribution of the effect size in $t$Meta follows the $t$ distribution, enabling that $t$Meta can simultaneously accommodate and detect outlying studies in a simple and adaptive manner. A simple and fast EM-type algorithm is developed for maximum likelihood estimation. Due to the mathematical tractability of the $t$ distribution, $t$Meta frees from numerical integration and allows for efficient optimization. Experiments on real data demonstrate that $t$Meta is compared favorably with related competitors in situations involving mild outliers. Moreover, in the presence of gross outliers, while related competitors may fail, $t$Meta continues to perform consistently and robustly.

The interaction of a protein with its environment can be understood and controlled via its 3D structure. Experimental methods for protein structure determination, such as X-ray crystallography or cryogenic electron microscopy, shed light on biological processes but introduce challenging inverse problems. Learning-based approaches have emerged as accurate and efficient methods to solve these inverse problems for 3D structure determination, but are specialized for a predefined type of measurement. Here, we introduce a versatile framework to turn raw biophysical measurements of varying types into 3D atomic models. Our method combines a physics-based forward model of the measurement process with a pretrained generative model providing a task-agnostic, data-driven prior. Our method outperforms posterior sampling baselines on both linear and non-linear inverse problems. In particular, it is the first diffusion-based method for refining atomic models from cryo-EM density maps.

Recent advances in probabilistic deep learning enable efficient amortized Bayesian inference in settings where the likelihood function is only implicitly defined by a simulation program (simulation-based inference; SBI). But how faithful is such inference if the simulation represents reality somewhat inaccurately, that is, if the true system behavior at test time deviates from the one seen during training? We conceptualize the types of such model misspecification arising in SBI and systematically investigate how the performance of neural posterior approximators gradually deteriorates as a consequence, making inference results less and less trustworthy. To notify users about this problem, we propose a new misspecification measure that can be trained in an unsupervised fashion (i.e., without training data from the true distribution) and reliably detects model misspecification at test time. Our experiments clearly demonstrate the utility of our new measure both on toy examples with an analytical ground-truth and on representative scientific tasks in cell biology, cognitive decision making, disease outbreak dynamics, and computer vision. We show how the proposed misspecification test warns users about suspicious outputs, raises an alarm when predictions are not trustworthy, and guides model designers in their search for better simulators.

In recent years, solving optimization problems involving black-box simulators has become a point of focus for the machine learning community due to their ubiquity in science and engineering. The simulators describe a forward process $f_{\mathrm{sim}}: (\psi, x) \rightarrow y$ from simulation parameters $\psi$ and input data $x$ to observations $y$, and the goal of the optimization problem is to find parameters $\psi$ that minimize a desired loss function. Sophisticated optimization algorithms typically require gradient information regarding the forward process, $f_{\mathrm{sim}}$, with respect to the parameters $\psi$. However, obtaining gradients from black-box simulators can often be prohibitively expensive or, in some cases, impossible. Furthermore, in many applications, practitioners aim to solve a set of related problems. Thus, starting the optimization ``ab initio", i.e. from scratch, each time might be inefficient if the forward model is expensive to evaluate. To address those challenges, this paper introduces a novel method for solving classes of similar black-box optimization problems by learning an active learning policy that guides a differentiable surrogate's training and uses the surrogate's gradients to optimize the simulation parameters with gradient descent. After training the policy, downstream optimization of problems involving black-box simulators requires up to $\sim$90\% fewer expensive simulator calls compared to baselines such as local surrogate-based approaches, numerical optimization, and Bayesian methods.

Current approaches to model-based offline Reinforcement Learning (RL) often incorporate uncertainty-based reward penalization to address the distributional shift problem. While these approaches have achieved some success, we argue that this penalization introduces excessive conservatism, potentially resulting in suboptimal policies through underestimation. We identify as an important cause of over-penalization the lack of a reliable uncertainty estimator capable of propagating uncertainties in the Bellman operator. The common approach to calculating the penalty term relies on sampling-based uncertainty estimation, resulting in high variance. To address this challenge, we propose a novel method termed Moment Matching Offline Model-Based Policy Optimization (MOMBO). MOMBO learns a Q-function using moment matching, which allows us to deterministically propagate uncertainties through the Q-function. We evaluate MOMBO's performance across various environments and demonstrate empirically that MOMBO is a more stable and sample-efficient approach.

High-dimensional Bayesian optimization (BO) tasks such as molecular design often require > 10,000 function evaluations before obtaining meaningful results. While methods like sparse variational Gaussian processes (SVGPs) reduce computational requirements in these settings, the underlying approximations result in suboptimal data acquisitions that slow the progress of optimization. In this paper we modify SVGPs to better align with the goals of BO: targeting informed data acquisition rather than global posterior fidelity. Using the framework of utility-calibrated variational inference, we unify GP approximation and data acquisition into a joint optimization problem, thereby ensuring optimal decisions under a limited computational budget. Our approach can be used with any decision-theoretic acquisition function and is compatible with trust region methods like TuRBO. We derive efficient joint objectives for the expected improvement and knowledge gradient acquisition functions in both the standard and batch BO settings. Our approach outperforms standard SVGPs on high-dimensional benchmark tasks in control and molecular design.

The diffusion bridge is a type of diffusion process that conditions on hitting a specific state within a finite time period. It has broad applications in fields such as Bayesian inference, financial mathematics, control theory, and shape analysis. However, simulating the diffusion bridge for natural data can be challenging due to both the intractability of the drift term and continuous representations of the data. Although several methods are available to simulate finite-dimensional diffusion bridges, infinite-dimensional cases remain unresolved. In the paper, we present a solution to this problem by merging score-matching techniques with operator learning, enabling a direct approach to score-matching for the infinite-dimensional bridge. We construct the score to be discretization invariant, which is natural given the underlying spatially continuous process. We conduct a series of experiments, ranging from synthetic examples with closed-form solutions to the stochastic nonlinear evolution of real-world biological shape data, and our method demonstrates high efficacy, particularly due to its ability to adapt to any resolution without extra training.