Proving algorithm-dependent generalization error bounds for gradient-type optimization methods has attracted significant attention recently in learning theory. However, most existing trajectory-based analyses require either restrictive assumptions on the learning rate (e.g., fast decreasing learning rate), or continuous injected noise (such as the Gaussian noise in Langevin dynamics). In this paper, we introduce a new discrete data-dependent prior to the PAC-Bayesian framework, and prove a high probability generalization bound of order $O(\frac{1}{n}\cdot \sum_{t=1}^T(\gamma_t/\varepsilon_t)^2\left\|{\mathbf{g}_t}\right\|^2)$ for Floored GD (i.e. a version of gradient descent with precision level $\varepsilon_t$), where $n$ is the number of training samples, $\gamma_t$ is the learning rate at step $t$, $\mathbf{g}_t$ is roughly the difference of the gradient computed using all samples and that using only prior samples. $\left\|{\mathbf{g}_t}\right\|$ is upper bounded by and and typical much smaller than the gradient norm $\left\|{\nabla f(W_t)}\right\|$. We remark that our bound holds for nonconvex and nonsmooth scenarios. Moreover, our theoretical results provide numerically favorable upper bounds of testing errors (e.g., $0.037$ on MNIST). Using a similar technique, we can also obtain new generalization bounds for certain variants of SGD. Furthermore, we study the generalization bounds for gradient Langevin Dynamics (GLD). Using the same framework with a carefully constructed continuous prior, we show a new high probability generalization bound of order $O(\frac{1}{n} + \frac{L^2}{n^2}\sum_{t=1}^T(\gamma_t/\sigma_t)^2)$ for GLD. The new $1/n^2$ rate is due to the concentration of the difference between the gradient of training samples and that of the prior.

Learning high-level causal representations together with a causal model from unstructured low-level data such as pixels is impossible from observational data alone. We prove under mild assumptions that this representation is however identifiable in a weakly supervised setting. This involves a dataset with paired samples before and after random, unknown interventions, but no further labels. We then introduce implicit latent causal models, variational autoencoders that represent causal variables and causal structure without having to optimize an explicit discrete graph structure. On simple image data, including a novel dataset of simulated robotic manipulation, we demonstrate that such models can reliably identify the causal structure and disentangle causal variables.

The Recurrent Neural Network (RNN) has been used to obtain state-of-the-art results in sequence modeling. This includes time series analysis, forecasting and natural language processing (NLP). Learn about why RNNs beat old-school machine learning algorithms like Hidden Markov Models. All of the materials required for this course can be downloaded and installed for FREE. We will do most of our work in Numpy, Matplotlib, and Tensorflow.

Pollutant exposure during gestation is a known and adverse factor for birth and health outcomes. However, the links between prenatal air pollution exposures and educational outcomes are less clear, in particular the critical windows of susceptibility during pregnancy. Using a large cohort of students in North Carolina, we study the link between prenatal daily $\mbox{PM}_{2.5}$ exposure and 4th end-of-grade reading scores. We develop and apply a locally adaptive and highly scalable Bayesian regression model for scalar responses with functional and scalar predictors. The proposed model pairs a B-spline basis expansion with dynamic shrinkage priors to capture both smooth and rapidly-changing features in the regression surface. The model is accompanied by a new decision analysis approach for functional regression that extracts the critical windows of susceptibility and guides the model interpretations. These tools help to identify and address broad limitations with the interpretability of functional regression models. Simulation studies demonstrate more accurate point estimation, more precise uncertainty quantification, and far superior window selection than existing approaches. Leveraging the proposed modeling, computational, and decision analysis framework, we conclude that prenatal $\mbox{PM}_{2.5}$ exposure during early and late pregnancy is most adverse for 4th end-of-grade reading scores.

Fog manufacturing can greatly enhance traditional manufacturing systems through distributed Fog computation units, which are governed by predictive computational workload offloading methods under different Industrial Internet architectures. It is known that the predictive offloading methods highly depend on accurate prediction and uncertainty quantification of runtime performance metrics, containing multivariate mixed-type responses (i.e., continuous, counting, binary). In this work, we propose a Bayesian sparse regression for multivariate mixed responses to enhance the prediction of runtime performance metrics and to enable the statistical inferences. The proposed method considers both group and individual variable selection to jointly model the mixed types of runtime performance metrics. The conditional dependency among multiple responses is described by a graphical model using the precision matrix, where a spike-and-slab prior is used to enable the sparse estimation of the graph. The proposed method not only achieves accurate prediction, but also makes the predictive model more interpretable with statistical inferences on model parameters and prediction in the Fog manufacturing. A simulation study and a real case example in a Fog manufacturing are conducted to demonstrate the merits of the proposed model.

Gaussian process (GP) regression is a flexible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that are related to the response. For this setting, we propose a novel, scalable algorithm, coined VGPR, which optimizes a penalized GP log-likelihood based on the Vecchia GP approximation, an ordered conditional approximation from spatial statistics that implies a sparse Cholesky factor of the precision matrix. We traverse the regularization path from strong to weak penalization, sequentially adding candidate covariates based on the gradient of the log-likelihood and deselecting irrelevant covariates via a new quadratic constrained coordinate descent algorithm. We propose Vecchia-based mini-batch subsampling, which provides unbiased gradient estimators. The resulting procedure is scalable to millions of responses and thousands of covariates. Theoretical analysis and numerical studies demonstrate the improved scalability and accuracy relative to existing methods.

Three key properties that are desired of trustworthy machine learning models deployed in high-stakes environments are fairness, explainability, and an ability to account for various kinds of "drift". While drifts in model accuracy, for example due to covariate shift, have been widely investigated, drifts in fairness metrics over time remain largely unexplored. In this paper, we propose FEAMOE, a novel "mixture-of-experts" inspired framework aimed at learning fairer, more explainable/interpretable models that can also rapidly adjust to drifts in both the accuracy and the fairness of a classifier. We illustrate our framework for three popular fairness measures and demonstrate how drift can be handled with respect to these fairness constraints. Experiments on multiple datasets show that our framework as applied to a mixture of linear experts is able to perform comparably to neural networks in terms of accuracy while producing fairer models. We then use the large-scale HMDA dataset and show that while various models trained on HMDA demonstrate drift with respect to both accuracy and fairness, FEAMOE can ably handle these drifts with respect to all the considered fairness measures and maintain model accuracy as well. We also prove that the proposed framework allows for producing fast Shapley value explanations, which makes computationally efficient feature attribution based explanations of model decisions readily available via FEAMOE.

We consider the problem of making AI agents that collaborate well with humans in partially observable fully cooperative environments given datasets of human behavior. Inspired by piKL, a human-data-regularized search method that improves upon a behavioral cloning policy without diverging far away from it, we develop a three-step algorithm that achieve strong performance in coordinating with real humans in the Hanabi benchmark. We first use a regularized search algorithm and behavioral cloning to produce a better human model that captures diverse skill levels. Then, we integrate the policy regularization idea into reinforcement learning to train a human-like best response to the human model. Finally, we apply regularized search on top of the best response policy at test time to handle outof-distribution challenges when playing with humans. We evaluate our method in two large scale experiments with humans. First, we show that our method outperforms experts when playing with a group of diverse human players in ad-hoc teams. Second, we show that our method beats a vanilla best response to behavioral cloning baseline by having experts play repeatedly with the two agents. One of the most fundamental goals of artificial intelligence research, especially multi-agent research, is to produce agents that can successfully collaborate with humans to achieve common goals. Although search and reinforcement learning (RL) from scratch without human knowledge have achieved impressive superhuman performance in competitive games (Silver et al., 2017; Brown & Sandholm, 2019), prior works (Hu et al., 2020; Carroll et al., 2019) have shown that agents produced by vanilla multi-agent reinforcement learning do not collaborate well with humans.

State-of-the-art (SOTA) semi-supervised learning (SSL) methods have been highly successful in leveraging a mix of labeled and unlabeled data by combining techniques of consistency regularization and pseudo-labeling. During pseudo-labeling, the model's predictions on unlabeled data are used for training and thus, model calibration is important in mitigating confirmation bias. Yet, many SOTA methods are optimized for model performance, with little focus directed to improve model calibration. In this work, we empirically demonstrate that model calibration is strongly correlated with model performance and propose to improve calibration via approximate Bayesian techniques. We introduce a family of new SSL models that optimizes for calibration and demonstrate their effectiveness across standard vision benchmarks of CIFAR-10, CIFAR-100 and ImageNet, giving up to 15.9% improvement in test accuracy. Furthermore, we also demonstrate their effectiveness in additional realistic and challenging problems, such as class-imbalanced datasets and in photonics science.

Recently, continual learning has received a lot of attention. One of the significant problems is the occurrence of \emph{concept drift}, which consists of changing probabilistic characteristics of the incoming data. In the case of the classification task, this phenomenon destabilizes the model's performance and negatively affects the achieved prediction quality. Most current methods apply statistical learning and similarity analysis over the raw data. However, similarity analysis in streaming data remains a complex problem due to time limitation, non-precise values, fast decision speed, scalability, etc. This article introduces a novel method for monitoring changes in the probabilistic distribution of multi-dimensional data streams. As a measure of the rapidity of changes, we analyze the popular Kullback-Leibler divergence. During the experimental study, we show how to use this metric to predict the concept drift occurrence and understand its nature. The obtained results encourage further work on the proposed methods and its application in the real tasks where the prediction of the future appearance of concept drift plays a crucial role, such as predictive maintenance.