Bayesian methods for learning Gaussian graphical models offer a robust framework that addresses model uncertainty and incorporates prior knowledge. Despite their theoretical strengths, the applicability of Bayesian methods is often constrained by computational needs, especially in modern contexts involving thousands of variables. To overcome this issue, we introduce two novel Markov chain Monte Carlo (MCMC) search algorithms that have a significantly lower computational cost than leading Bayesian approaches. Our proposed MCMC-based search algorithms use the marginal pseudo-likelihood approach to bypass the complexities of computing intractable normalizing constants and iterative precision matrix sampling. These algorithms can deliver reliable results in mere minutes on standard computers, even for large-scale problems with one thousand variables. Furthermore, our proposed method is capable of addressing model uncertainty by efficiently exploring the full posterior graph space. Our simulation study indicates that the proposed algorithms, particularly for large-scale sparse graphs, outperform the leading Bayesian approaches in terms of computational efficiency and precision. The implementation supporting the new approach is available through the R package BDgraph.

The core principle of Variational Inference (VI) is to convert the statistical inference problem of computing complex posterior probability densities into a tractable optimization problem. This property enables VI to be faster than several sampling-based techniques. However, the traditional VI algorithm is not scalable to large data sets and is unable to readily infer out-of-bounds data points without re-running the optimization process. Recent developments in the field, like stochastic-, black box-, and amortized-VI, have helped address these issues. Generative modeling tasks nowadays widely make use of amortized VI for its efficiency and scalability, as it utilizes a parameterized function to learn the approximate posterior density parameters. In this paper, we review the mathematical foundations of various VI techniques to form the basis for understanding amortized VI. Additionally, we provide an overview of the recent trends that address several issues of amortized VI, such as the amortization gap, generalization issues, inconsistent representation learning, and posterior collapse. Finally, we analyze alternate divergence measures that improve VI optimization.

Neural networks have become a powerful tool as surrogate models to provide numerical solutions for scientific problems with increased computational efficiency. This efficiency can be advantageous for numerically challenging problems where time to solution is important or when evaluation of many similar analysis scenarios is required. One particular area of scientific interest is the setting of inverse problems, where one knows the forward dynamics of a system are described by a partial differential equation and the task is to infer properties of the system given (potentially noisy) observations of these dynamics. We consider the inverse problem of inferring the location of a wave source on a square domain, given a noisy solution to the 2-D acoustic wave equation. Under the assumption of Gaussian noise, a likelihood function for source location can be formulated, which requires one forward simulation of the system per evaluation. Using a standard neural network as a surrogate model makes it computationally feasible to evaluate this likelihood several times, and so Markov Chain Monte Carlo methods can be used to evaluate the posterior distribution of the source location. We demonstrate that this method can accurately infer source-locations from noisy data.

Community Question-Answering (CQA) portals serve as a valuable tool for helping users within an organization. However, making them accessible to non-English-speaking users continues to be a challenge. Translating questions can broaden the community's reach, benefiting individuals with similar inquiries in various languages. Translating questions using Neural Machine Translation (NMT) poses more challenges, especially in noisy environments, where the grammatical correctness of the questions is not monitored. These questions may be phrased as statements by non-native speakers, with incorrect subject-verb order and sometimes even missing question marks. Creating a synthetic parallel corpus from such data is also difficult due to its noisy nature. To address this issue, we propose a training methodology that fine-tunes the NMT system only using source-side data. Our approach balances adequacy and fluency by utilizing a loss function that combines BERTScore and Masked Language Model (MLM) Score. Our method surpasses the conventional Maximum Likelihood Estimation (MLE) based fine-tuning approach, which relies on synthetic target data, by achieving a 1.9 BLEU score improvement. Our model exhibits robustness while we add noise to our baseline, and still achieve 1.1 BLEU improvement and large improvements on TER and BLEURT metrics. Our proposed methodology is model-agnostic and is only necessary during the training phase. We make the codes and datasets publicly available at \url{https://www.iitp.ac.in/~ai-nlp-ml/resources.html#DomainAdapt} for facilitating further research.

In a previous work we introduced, in the context of gravitational wave science, an initial study on an automated domain-decomposition approach for reduced basis through hp-greedy refinement. The approach constructs local reduced bases of lower dimensionality than global ones, with the same or higher accuracy. These ``light'' local bases should imply both faster evaluations when predicting new waveforms and faster data analysis, in particular faster statistical inference (the forward and inverse problems, respectively). In this approach, however, we have previously found important dependence on several hyperparameters, which do not appear in global reduced basis. This naturally leads to the problem of hyperparameter optimization (HPO), which is the subject of this paper. We tackle the problem through a Bayesian optimization, and show its superiority when compared to grid or random searches. We find that for gravitational waves from the collision of two spinning but non-precessing black holes, for the same accuracy, local hp-greedy reduced bases with HPO have a lower dimensionality of up to $4 \times$ for the cases here studied, depending on the desired accuracy. This factor should directly translate in a parameter estimation speedup, for instance. Such acceleration might help in the near real-time requirements for electromagnetic counterparts of gravitational waves from compact binary coalescences. In addition, we find that the Bayesian approach used in this paper for HPO is two orders of magnitude faster than, for example, a grid search, with about a $100 \times$ acceleration. The code developed for this project is available as open source from public repositories.

Data is the lifeblood of machine learning, yet for many firms, obtaining datasets of sufficient quality remains a challenge, with them being naturally distributed amongst owners with heterogeneous characteristics (e.g., privacy preferences). This has motivated several developments in the field of collaborative analytics, also known as federated learning (Figure 1a), where models are trained on local servers without the need for data centralization, thereby preserving privacy and distributing the computational burden (Kairouz et al., 2019). However, this framework provides only an incentive-free means for data sharing, relying on the critical assumption that owners are willing to collaborate (i.e., by sharing their private information) altruistically. This rather strong assumption may be violated if owners are competitors in a downstream market environment (Gal-Or, 1985). Consequently, a fruitful area of research has emerged that proposes to instead commoditize data within a market-based framework, where compensation (e.g., remuneration) can be used as an incentive for collaboration (Bergemann and Bonatti, 2019).

The posterior in probabilistic programs with stochastic support decomposes as a weighted sum of the local posterior distributions associated with each possible program path. We show that making predictions with this full posterior implicitly performs a Bayesian model averaging (BMA) over paths. This is potentially problematic, as model misspecification can cause the BMA weights to prematurely collapse onto a single path, leading to sub-optimal predictions in turn. To remedy this issue, we propose alternative mechanisms for path weighting: one based on stacking and one based on ideas from PAC-Bayes. We show how both can be implemented as a cheap post-processing step on top of existing inference engines. In our experiments, we find them to be more robust and lead to better predictions compared to the default BMA weights.

Conditional generative models became a very powerful tool to sample from Bayesian inverse problem posteriors. It is well-known in classical Bayesian literature that posterior measures are quite robust with respect to perturbations of both the prior measure and the negative log-likelihood, which includes perturbations of the observations. However, to the best of our knowledge, the robustness of conditional generative models with respect to perturbations of the observations has not been investigated yet. In this paper, we prove for the first time that appropriately learned conditional generative models provide robust results for single observations.

Can non-programmers annotate natural language utterances with complex programs that represent their meaning? We introduce APEL, a framework in which non-programmers select among candidate programs generated by a seed semantic parser (e.g., Codex). Since they cannot understand the candidate programs, we ask them to select indirectly by examining the programs' input-ouput examples. For each utterance, APEL actively searches for a simple input on which the candidate programs tend to produce different outputs. It then asks the non-programmers only to choose the appropriate output, thus allowing us to infer which program is correct and could be used to fine-tune the parser. As a first case study, we recruited human non-programmers to use APEL to re-annotate SPIDER, a text-to-SQL dataset. Our approach achieved the same annotation accuracy as the original expert annotators (75%) and exposed many subtle errors in the original annotations.

Model reparametrization, which follows the change-of-variable rule of calculus, is a popular way to improve the training of neural nets. But it can also be problematic since it can induce inconsistencies in, e.g., Hessian-based flatness measures, optimization trajectories, and modes of probability densities. This complicates downstream analyses: e.g. one cannot definitively relate flatness with generalization since arbitrary reparametrization changes their relationship. In this work, we study the invariance of neural nets under reparametrization from the perspective of Riemannian geometry. From this point of view, invariance is an inherent property of any neural net if one explicitly represents the metric and uses the correct associated transformation rules. This is important since although the metric is always present, it is often implicitly assumed as identity, and thus dropped from the notation, then lost under reparametrization. We discuss implications for measuring the flatness of minima, optimization, and for probability-density maximization. Finally, we explore some interesting directions where invariance is useful.