Contextual Bandits find important use cases in various real-life scenarios such as online advertising, recommendation systems, healthcare, etc. However, most of the algorithms use flat feature vectors to represent context whereas, in the real world, there is a varying number of objects and relations among them to model in the context. For example, in a music recommendation system, the user context contains what music they listen to, which artists create this music, the artist albums, etc. Adding richer relational context representations also introduces a much larger context space making exploration-exploitation harder. To improve the efficiency of exploration-exploitation knowledge about the context can be infused to guide the exploration-exploitation strategy. Relational context representations allow a natural way for humans to specify knowledge owing to their descriptive nature. We propose an adaptation of Knowledge Infused Policy Gradients to the Contextual Bandit setting and a novel Knowledge Infused Policy Gradients Upper Confidence Bound algorithm and perform an experimental analysis of a simulated music recommendation dataset and various real-life datasets where expert knowledge can drastically reduce the total regret and where it cannot.

Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often treat them separately, and thus develop problem-specific algorithms and their analyses. Among various exciting developments, simple SGD-type updates (potentially on multiple variables) are still prevalent in solving this class of nested problems, but they are believed to have slower convergence rate compared to that of the non-nested problems. This paper unifies several SGD-type updates for stochastic nested problems into a single SGD approach that we term ALternating Stochastic gradient dEscenT (ALSET) method. By leveraging the hidden smoothness of the problem, this paper presents a tighter analysis of ALSET for stochastic nested problems. Under the new analysis, to achieve an $\epsilon$-stationary point of the nested problem, it requires ${\cal O}(\epsilon^{-2})$ samples. Under certain regularity conditions, applying our results to stochastic compositional, min-max and reinforcement learning problems either improves or matches the best-known sample complexity in the respective cases. Our results explain why simple SGD-type algorithms in stochastic nested problems all work very well in practice without the need for further modifications.

The large-scale data stream problem refers to high-speed information flow which cannot be processed in scalable manner under a traditional computing platform. This problem also imposes expensive labelling cost making the deployment of fully supervised algorithms unfeasible. On the other hand, the problem of semi-supervised large-scale data streams is little explored in the literature because most works are designed in the traditional single-node computing environments while also being fully supervised approaches. This paper offers Weakly Supervised Scalable Teacher Forcing Network (WeScatterNet) to cope with the scarcity of labelled samples and the large-scale data streams simultaneously. WeScatterNet is crafted under distributed computing platform of Apache Spark with a data-free model fusion strategy for model compression after parallel computing stage. It features an open network structure to address the global and local drift problems while integrating a data augmentation, annotation and auto-correction ($DA^3$) method for handling partially labelled data streams. The performance of WeScatterNet is numerically evaluated in the six large-scale data stream problems with only $25\%$ label proportions. It shows highly competitive performance even if compared with fully supervised learners with $100\%$ label proportions.

While multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model. We demonstrate our framework using several academic case studies and two finite element (FE) model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.

While the success of stochastic gradient methods for solving empirical risk minimization has motivated their adoption across much of machine learning, increasing privacy risks in data-intensive tasks have made applying them more challenging [DMNS06]: gradients can leak users' data, intermediate models can compromise individuals, and even final trained models may be non-private without substantial care. This motivates a growing line of work developing private variants of stochastic gradient descent (SGD), where algorithms guarantee differential privacy by perturbing individual gradients with random noise [DJW13; ST13b; ACGMMTZ16; DJW18; BFTT19; FKT20]. Yet these noise addition procedures typically fail to reflect the geometry underlying the optimization problem, which in non-private cases is essential: for high-dimensional problems with sparse parameters, mirror descent and its variants [BT03; NJLS09] are essential, while in the large-scale stochastic settings prevalent in deep learning, AdaGrad and other adaptive variants [DHS11] provide stronger theoretical and practical performance. Even more, methods that do not adapt (or do not leverage geometry) can be provably sub-optimal, in that there exist problems where their convergence is much slower than adaptive variants that reflect appropriate geometry [LD19]. To address these challenges, we introduce Pagan (Private AdaGrad with Adaptive Noise), a new differentially private variant of stochastic gradient descent and AdaGrad.

Sparse Principal Component Analysis (SPCA) is widely used in data processing and dimension reduction; it uses the lasso to produce modified principal components with sparse loadings for better interpretability. However, sparse PCA never considers an additional grouping structure where the loadings share similar coefficients (i.e., feature grouping), besides a special group with all coefficients being zero (i.e., feature selection). In this paper, we propose a novel method called Feature Grouping and Sparse Principal Component Analysis (FGSPCA) which allows the loadings to belong to disjoint homogeneous groups, with sparsity as a special case. The proposed FGSPCA is a subspace learning method designed to simultaneously perform grouping pursuit and feature selection, by imposing a non-convex regularization with naturally adjustable sparsity and grouping effect. To solve the resulting non-convex optimization problem, we propose an alternating algorithm that incorporates the difference-of-convex programming, augmented Lagrange and coordinate descent methods. Additionally, the experimental results on real data sets show that the proposed FGSPCA benefits from the grouping effect compared with methods without grouping effect.

We present a new second-order oracle bound for the expected risk of a weighted majority vote. The bound is based on a novel parametric form of the Chebyshev-Cantelli inequality (a.k.a.\ one-sided Chebyshev's), which is amenable to efficient minimization. The new form resolves the optimization challenge faced by prior oracle bounds based on the Chebyshev-Cantelli inequality, the C-bounds [Germain et al., 2015], and, at the same time, it improves on the oracle bound based on second order Markov's inequality introduced by Masegosa et al. [2020]. We also derive the PAC-Bayes-Bennett inequality, which we use for empirical estimation of the oracle bound. The PAC-Bayes-Bennett inequality improves on the PAC-Bayes-Bernstein inequality by Seldin et al. [2012]. We provide an empirical evaluation demonstrating that the new bounds can improve on the work by Masegosa et al. [2020]. Both the parametric form of the Chebyshev-Cantelli inequality and the PAC-Bayes-Bennett inequality may be of independent interest for the study of concentration of measure in other domains.

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some extent. However, real-world data may display structures that can not be fully captured by these simple functions. In addition, existing methods treat complex and simple samples equally. By contrast, a learning pattern typically adopted by human beings is to learn from simple to complex and less to more. Based on this principle, we propose a novel method called Self-paced PCA (SPCA) to further reduce the effect of noise and outliers. Notably, the complexity of each sample is calculated at the beginning of each iteration in order to integrate samples from simple to more complex into training. Based on an alternating optimization, SPCA finds an optimal projection matrix and filters out outliers iteratively. Theoretical analysis is presented to show the rationality of SPCA. Extensive experiments on popular data sets demonstrate that the proposed method can improve the state of-the-art results considerably.

High-resolution manometry (HRM) is the primary procedure used to diagnose esophageal motility disorders. Its interpretation and classification includes an initial evaluation of swallow-level outcomes and then derivation of a study-level diagnosis based on Chicago Classification (CC), using a tree-like algorithm. This diagnostic approach on motility disordered using HRM was mirrored using a multi-stage modeling framework developed using a combination of various machine learning approaches. Specifically, the framework includes deep-learning models at the swallow-level stage and feature-based machine learning models at the study-level stage. In the swallow-level stage, three models based on convolutional neural networks (CNNs) were developed to predict swallow type, swallow pressurization, and integrated relaxation pressure (IRP). At the study-level stage, model selection from families of the expert-knowledge-based rule models, xgboost models and artificial neural network(ANN) models were conducted, with the latter two model designed and augmented with motivation from the export knowledge. A simple model-agnostic strategy of model balancing motivated by Bayesian principles was utilized, which gave rise to model averaging weighted by precision scores. The averaged (blended) models and individual models were compared and evaluated, of which the best performance on test dataset is 0.81 in top-1 prediction, 0.92 in top-2 predictions. This is the first artificial-intelligence-style model to automatically predict CC diagnosis of HRM study from raw multi-swallow data. Moreover, the proposed modeling framework could be easily extended to multi-modal tasks, such as diagnosis of esophageal patients based on clinical data from both HRM and functional luminal imaging probe panometry (FLIP).

We empirically show that the test error of deep networks can be estimated by simply training the same architecture on the same training set but with a different run of Stochastic Gradient Descent (SGD), and measuring the disagreement rate between the two networks on unlabeled test data. This builds on -- and is a stronger version of -- the observation in Nakkiran & Bansal '20, which requires the second run to be on an altogether fresh training set. We further theoretically show that this peculiar phenomenon arises from the \emph{well-calibrated} nature of \emph{ensembles} of SGD-trained models. This finding not only provides a simple empirical measure to directly predict the test error using unlabeled test data, but also establishes a new conceptual connection between generalization and calibration.