We consider the problem of learning Bayesian networks optimally, when subject to background knowledge in the form of ancestral constraints. Our approach is based on a recently proposed framework for optimal structure learning based on non-decomposable scores, which is general enough to accommodate ancestral constraints. The proposed framework exploits oracles for learning structures using decomposable scores, which cannot accommodate ancestral constraints since they are non-decomposable. We show how to empower these oracles by passing them decomposable constraints that they can handle, which are inferred from ancestral constraints that they cannot handle. Empirically, we demonstrate that our approach can be orders-of-magnitude more efficient than alternative frameworks, such as those based on integer linear programming.

We present the first application of the median of means in a PAC exploration algorithm for MDPs. Using the median of means allows us to significantly reduce the dependence of our bounds on the range of values that the value function can take, while introducing a dependence on the (potentially much smaller) variance of the Bellman operator. Additionally, our algorithm is the first algorithm with PAC bounds that can be applied to MDPs with unbounded rewards.

Bayes type methods, which would otherwise be well suited to the i.i.d. Our focus in this paper is not to explore the generalities of finite-dimensional processes.

Variational approaches are often used to approximate intractable posteriors or normalization constants in hierarchical latent variable models. While often effective in practice, it is known that the approximation error can be arbitrarily large. We propose a new class of bounds on the marginal log-likelihood of directed latent variable models. Our approach relies on random projections to simplify the posterior. In contrast to standard variational methods, our bounds are guaranteed to be tight with high probability. We provide a new approach for learning latent variable models based on optimizing our new bounds on the log-likelihood. We demonstrate empirical improvements on benchmark datasets in vision and language for sigmoid belief networks, where a neural network is used to approximate the posterior.

When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special case of regularized M-estimation, as a surrogate. However, MAP is suboptimal in high dimensions, when the number of unknown signal components is similar to the number of measurements. In this work we demonstrate, when the signal distribution and the likelihood function associated with the noise are both log-concave, that optimal MMSE performance is asymptotically achievable via another M-estimation procedure. This procedure involves minimizing convex loss and regularizer functions that are nonlinearly smoothed versions of the widely applied MAP optimization problem. Our findings provide a new heuristic derivation and interpretation for recent optimal M-estimators found in the setting of linear measurements and additive noise, and further extend these results to nonlinear measurements with non-additive noise. We numerically demonstrate superior performance of our optimal M-estimators relative to MAP. Overall, at the heart of our work is the revelation of a remarkable equivalence between two seemingly very different computational problems: namely that of high dimensional Bayesian integration underlying MMSE inference, and high dimensional convex optimization underlying M-estimation. In essence we show that the former difficult integral may be computed by solving the latter, simpler optimization problem.

Active learning enables us to reduce the annotation cost by adaptively selecting unlabeled instances to be labeled. For pool-based active learning, several effective methods with theoretical guarantees have been developed through maximizing some utility function satisfying adaptive submodularity. In contrast, there have been few methods for stream-based active learning based on adaptive submodularity. In this paper, we propose a new class of utility functions, policy-adaptive submodular functions, which includes many existing adaptive submodular functions appearing in real world problems. We provide a general framework based on policy-adaptive submodularity that makes it possible to convert existing poolbased methods to stream-based methods and give theoretical guarantees on their performance. In addition we empirically demonstrate their effectiveness by comparing with existing heuristics on common benchmark datasets.

Recurrent neural networks (RNNs) stand at the forefront of many recent developments in deep learning. Yet a major difficulty with these models is their tendency to overfit, with dropout shown to fail when applied to recurrent layers.

Estimating patient's clinical state from multiple concurrent physiological streams plays an important role in determining if a therapeutic intervention is necessary and for triaging patients in the hospital. In this paper we construct a non-parametric learning algorithm to estimate the clinical state of a patient. The algorithm addresses several known challenges with clinical state estimation such as eliminating the bias introduced by therapeutic intervention censoring, increasing the timeliness of state estimation while ensuring a sufficient accuracy, and the ability to detect anomalous clinical states. These benefits are obtained by combining the tools of non-parametric Bayesian inference, permutation testing, and generalizations of the empirical Bernstein inequality. The algorithm is validated using real-world data from a cancer ward in a large academic hospital.

We propose an operator learning approach to accelerate geometric Markov chain Monte Carlo (MCMC) for solving infinite-dimensional nonlinear Bayesian inverse problems. While geometric MCMC employs high-quality proposals that adapt to posterior local geometry, it requires computing local gradient and Hessian information of the log-likelihood, incurring a high cost when the parameter-to-observable (PtO) map is defined through expensive model simulations. We consider a delayed-acceptance geometric MCMC method driven by a neural operator surrogate of the PtO map, where the proposal is designed to exploit fast surrogate approximations of the log-likelihood and, simultaneously, its gradient and Hessian. To achieve a substantial speedup, the surrogate needs to be accurate in predicting both the observable and its parametric derivative (the derivative of the observable with respect to the parameter). Training such a surrogate via conventional operator learning using input--output samples often demands a prohibitively large number of model simulations. In this work, we present an extension of derivative-informed operator learning [O'Leary-Roseberry et al., J. Comput. Phys., 496 (2024)] using input--output--derivative training samples. Such a learning method leads to derivative-informed neural operator (DINO) surrogates that accurately predict the observable and its parametric derivative at a significantly lower training cost than the conventional method. Cost and error analysis for reduced basis DINO surrogates are provided. Numerical studies on PDE-constrained Bayesian inversion demonstrate that DINO-driven MCMC generates effective posterior samples 3--9 times faster than geometric MCMC and 60--97 times faster than prior geometry-based MCMC. Furthermore, the training cost of DINO surrogates breaks even after collecting merely 10--25 effective posterior samples compared to geometric MCMC.

In the context of developing nations like India, traditional business to business (B2B) commerce heavily relies on the establishment of robust relationships, trust, and credit arrangements between buyers and sellers. Consequently, ecommerce enterprises frequently. Established in 2016 with a vision to revolutionize trade in India through technology, Udaan is the countrys largest business to business ecommerce platform. Udaan operates across diverse product categories, including lifestyle, electronics, home and employ telecallers to cultivate buyer relationships, streamline order placement procedures, and promote special promotions. The accurate anticipation of buyer order placement behavior emerges as a pivotal factor for attaining sustainable growth, heightening competitiveness, and optimizing the efficiency of these telecallers. To address this challenge, we have employed an ensemble approach comprising XGBoost and a modified version of Poisson Gamma model to predict customer order patterns with precision. This paper provides an in-depth exploration of the strategic fusion of machine learning and an empirical Bayesian approach, bolstered by the judicious selection of pertinent features. This innovative approach has yielded a remarkable 3 times increase in customer order rates, show casing its potential for transformative impact in the ecommerce industry.