Dynamic mechanism design has garnered significant attention from both computer scientists and economists in recent years. By allowing agents to interact with the seller over multiple rounds, where agents' reward functions may change with time and are state-dependent, the framework is able to model a rich class of real-world problems. In these works, the interaction between agents and sellers is often assumed to follow a Markov Decision Process (MDP). We focus on the setting where the reward and transition functions of such an MDP are not known a priori, and we are attempting to recover the optimal mechanism using an a priori collected data set. In the setting where the function approximation is employed to handle large state spaces, with only mild assumptions on the expressiveness of the function class, we are able to design a dynamic mechanism using offline reinforcement learning algorithms. Moreover, learned mechanisms approximately have three key desiderata: efficiency, individual rationality, and truthfulness. Our algorithm is based on the pessimism principle and only requires a mild assumption on the coverage of the offline data set. To the best of our knowledge, our work provides the first offline RL algorithm for dynamic mechanism design without assuming uniform coverage.

In this paper, we study the problem of inferring spatially-varying Gaussian Markov random fields (SV-GMRF) where the goal is to learn a network of sparse, context-specific GMRFs representing network relationships between genes. An important application of SV-GMRFs is in inference of gene regulatory networks from spatially-resolved transcriptomics datasets. The current work on inference of SV-GMRFs are based on the regularized maximum likelihood estimation (MLE) and suffer from overwhelmingly high computational cost due to their highly nonlinear nature. To alleviate this challenge, we propose a simple and efficient optimization problem in lieu of MLE that comes equipped with strong statistical and computational guarantees. Our proposed optimization problem is extremely efficient in practice: we can solve instances of SV-GMRFs with more than 2 million variables in less than 2 minutes. We apply the developed framework to study how gene regulatory networks in Glioblastoma are spatially rewired within tissue, and identify prominent activity of the transcription factor HES4 and ribosomal proteins as characterizing the gene expression network in the tumor peri-vascular niche that is known to harbor treatment resistant stem cells.

Before delegating a task to an autonomous system, a human operator may want a guarantee about the behavior of the system. This paper extends previous work on conformal prediction for functional data and conformalized quantile regression to provide conformal prediction intervals over the future behavior of an autonomous system executing a fixed control policy on a Markov Decision Process (MDP). The prediction intervals are constructed by applying conformal corrections to prediction intervals computed by quantile regression. The resulting intervals guarantee that with probability $1-\delta$ the observed trajectory will lie inside the prediction interval, where the probability is computed with respect to the starting state distribution and the stochasticity of the MDP. The method is illustrated on MDPs for invasive species management and StarCraft2 battles.

Machine learning is one of those fields that anyone learning data science should know. If you're new to data science, you probably must've heard of the words "algorithm" or "model" without knowing how they're related to machine learning. Machine learning algorithms are categorized as supervised or unsupervised. Supervised learning algorithms model the relationship between labeled input and output data (aka target). This model is then used to predict the label of new observations using new labeled input data.

We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the correlated error, and the variance of the noise based on maximizing a marginal likelihood function. Our method involves suitably reducing the dimensionality of the hyperparameter space to simplify the estimation procedure to a univariate root-finding problem. Moreover, we derive bounds and asymptotes of the marginal likelihood function and its derivatives, which are useful to narrowing the initial range of the hyperparameter search. Using numerical examples, we demonstrate the computational advantages and robustness of the presented approach compared to traditional parameter optimization.

We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in parallel in a single step and the magnitude of changes is controlled by a stepsize. This allows a cheap and efficient exploration in the space of high-dimensional and strongly correlated variables. We prove the efficiency of DLP by showing that the asymptotic bias of its stationary distribution is zero for log-quadratic distributions, and is small for distributions that are close to being log-quadratic. With DLP, we develop several variants of sampling algorithms, including unadjusted, Metropolis-adjusted, stochastic and preconditioned versions. DLP outperforms many popular alternatives on a wide variety of tasks, including Ising models, restricted Boltzmann machines, deep energy-based models, binary neural networks and language generation.

In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent variables associated with each data dimension. The nonnegativity constraint for the latent factors is handled by choosing priors with support on the nonnegative subspace. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including MovieLens 100K and MovieLens 1M with different sizes and dimensions and show that the proposed Bayesian NMF GRRN model leads to better predictions and avoids overfitting compared to existing Bayesian NMF approaches.

We consider the problem of deciding how best to target and prioritize existing vaccines that may offer protection against new variants of an infectious disease. Sequential experiments are a promising approach; however, challenges due to delayed feedback and the overall ebb and flow of disease prevalence make available methods inapplicable for this task. We present a method, partial likelihood Thompson sampling, that can handle these challenges. Our method involves running Thompson sampling with belief updates determined by partial likelihood each time we observe an event. To test our approach, we ran a semi-synthetic experiment based on 200 days of COVID-19 infection data in the US.

Making predictions robust is an important challenge. A separate challenge in federated learning (FL) is to reduce the number of communication rounds, particularly since doing so reduces performance in heterogeneous data settings. To tackle both issues, we take a Bayesian perspective on the problem of learning a global model. We show how the global predictive posterior can be approximated using client predictive posteriors. This is unlike other works which aggregate the local model space posteriors into the global model space posterior, and are susceptible to high approximation errors due to the posterior's high dimensional multimodal nature. In contrast, our method performs the aggregation on the predictive posteriors, which are typically easier to approximate owing to the low-dimensionality of the output space. We present an algorithm based on this idea, which performs MCMC sampling at each client to obtain an estimate of the local posterior, and then aggregates these in one round to obtain a global ensemble model. Through empirical evaluation on several classification and regression tasks, we show that despite using one round of communication, the method is competitive with other FL techniques, and outperforms them on heterogeneous settings. The code is publicly available at https://github.com/hasanmohsin/FedPredSpace_1Round.

Tensor decompositions have proven to be effective in analyzing the structure of multidimensional data. However, most of these methods require a key parameter: the number of desired components. In the case of the CANDECOMP/PARAFAC decomposition (CPD), this value is known as the canonical rank and greatly affects the quality of the results. Existing methods use heuristics or Bayesian methods to estimate this value by repeatedly calculating the CPD, making them extremely computationally expensive. In this work, we propose FRAPPE and Self-FRAPPE: a cheaply supervised and a self-supervised method to estimate the canonical rank of a tensor without ever having to compute the CPD. We call FRAPPE cheaply supervised because it uses a fully synthetic training set without requiring real-world examples. We evaluate these methods on synthetic tensors, real tensors of known rank, and the weight tensor of a convolutional neural network. We show that FRAPPE and Self-FRAPPE offer large improvements in both effectiveness and speed, with a respective $15\%$ and $10\%$ improvement in MAPE and an $4000\times$ and $13\times$ improvement in evaluation speed over the best-performing baseline.