In this work, we consider the deterministic optimization using random projections as a statistical estimation problem, where the squared distance between the predictions from the estimator and the true solution is the error metric. In approximately solving a large scale least squares problem using Gaussian sketches, we show that the sketched solution has a conditional Gaussian distribution with the true solution as its mean. Firstly, tight worst case error lower bounds with explicit constants are derived for any estimator using the Gaussian sketch, and the classical sketching is shown to be the optimal unbiased estimator. For biased estimators, the lower bound also incorporates prior knowledge about the true solution. Secondly, we use the James-Stein estimator to derive an improved estimator for the least squares solution using the Gaussian sketch. An upper bound on the expected error of this estimator is derived, which is smaller than the error of the classical Gaussian sketch solution for any given data. The upper and lower bounds match when the SNR of the true solution is known to be small and the data matrix is well conditioned. Empirically, this estimator achieves smaller error on simulated and real datasets, and works for other common sketching methods as well.

The systematic minimization of the quantifiable uncertainty, or risk [22], is one of the core objectives in all disciplines involving decision-making, e.g., economics and finance. Within machine learning contexts, strategies for risk-aversion have been most actively studied under sequential decision-making and reinforcement learning frameworks [21, 8], giving birth to a number of algorithms based on Markov decision processes (MDPs) and multi-armed bandits. In those works, various risk-averse measures of loss have been used as a minimization objective, instead of the risk-neutral expected loss; popular risk measures include entropic risk [21, 6, 7], mean-variance [39, 13, 28], and a slightly more modern alternative known as conditional value-at-risk (CVaR [15, 10, 42]). Yet, with growing interest to the societal impacts of machine intelligence, the importance of risk-aversion under non-sequential scenarios has also been spotlighted recently. For instance, Williamson and Menon [45] give an axiomatic characterization of the fairness risk measures, and propose a convex fairness-aware objective based on CVaR.

Reinforcement learning algorithms can acquire policies for complex tasks autonomously. However, the number of samples required to learn a diverse set of skills can be prohibitively large. While meta-reinforcement learning methods have enabled agents to leverage prior experience to adapt quickly to new tasks, their performance depends crucially on how close the new task is to the previously experienced tasks. Current approaches are either not able to extrapolate well, or can do so at the expense of requiring extremely large amounts of data for on-policy meta-training. In this work, we present model identification and experience relabeling (MIER), a meta-reinforcement learning algorithm that is both efficient and extrapolates well when faced with out-of-distribution tasks at test time. Our method is based on a simple insight: we recognize that dynamics models can be adapted efficiently and consistently with off-policy data, more easily than policies and value functions. These dynamics models can then be used to continue training policies and value functions for out-of-distribution tasks without using meta-reinforcement learning at all, by generating synthetic experience for the new task.

Many important questions about a model cannot be answered just by explaining how much each feature contributes to its output. To answer a broader set of questions, we generalize a popular, mathematically well-grounded explanation technique, Shapley Additive Explanations (SHAP). Our new method - Generalized Shapley Additive Explanations (G-SHAP) - produces many additional types of explanations, including: 1) General classification explanations; Why is this sample more likely to belong to one class rather than another? 2) Intergroup differences; Why do our model's predictions differ between groups of observations? 3) Model failure; Why does our model perform poorly on a given sample? We formally define these types of explanations and illustrate their practical use on real data.

Biomolecular graph analysis has recently gained much attention in the emerging field of geometric deep learning. While numerous approaches aim to train classifiers that accurately predict molecular properties from graphs that encode their structure, an equally important task is to organize biomolecular graphs in ways that expose meaningful relations and variations between them. We propose a geometric scattering autoencoder (GSAE) network for learning such graph embeddings. Our embedding network first extracts rich graph features using the recently proposed geometric scattering transform. Then, it leverages a semi-supervised variational autoencoder to extract a low-dimensional embedding that retains the information in these features that enable prediction of molecular properties as well as characterize graphs. Our approach is based on the intuition that geometric scattering generates multi-resolution features with in-built invariance to deformations, but as they are unsupervised, these features may not be tuned for optimally capturing relevant domain-specific properties. We demonstrate the effectiveness of our approach to data exploration of RNA foldings. Like proteins, RNA molecules can fold to create low energy functional structures such as hairpins, but the landscape of possible folds and fold sequences are not well visualized by existing methods. We show that GSAE organizes RNA graphs both by structure and energy, accurately reflecting bistable RNA structures. Furthermore, it enables interpolation of embedded molecule sequences mimicking folding trajectories. Finally, using an auxiliary inverse-scattering model, we demonstrate our ability to generate synthetic RNA graphs along the trajectory thus providing hypothetical folding sequences for further analysis.

With the rapid growth and prevalence of social network applications (Apps) in recent years, understanding user engagement has become increasingly important, to provide useful insights for future App design and development. While several promising neural modeling approaches were recently pioneered for accurate user engagement prediction, their black-box designs are unfortunately limited in model explainability. In this paper, we study a novel problem of explainable user engagement prediction for social network Apps. First, we propose a flexible definition of user engagement for various business scenarios, based on future metric expectations. Next, we design an end-to-end neural framework, FATE, which incorporates three key factors that we identify to influence user engagement, namely friendships, user actions, and temporal dynamics to achieve explainable engagement predictions. FATE is based on a tensor-based graph neural network (GNN), LSTM and a mixture attention mechanism, which allows for (a) predictive explanations based on learned weights across different feature categories, (b) reduced network complexity, and (c) improved performance in both prediction accuracy and training/inference time. We conduct extensive experiments on two large-scale datasets from Snapchat, where FATE outperforms state-of-the-art approaches by ${\approx}10\%$ error and ${\approx}20\%$ runtime reduction. We also evaluate explanations from FATE, showing strong quantitative and qualitative performance.

Clustering and prediction are two primary tasks in the fields of unsupervised and supervised learning, respectively. Although much of the recent advances in machine learning have been centered around those two tasks, the interdependent, mutually beneficial relationship between them is rarely explored. One could reasonably expect appropriately clustering the data would aid the downstream prediction task and, conversely, a better prediction performance for the downstream task could potentially inform a more appropriate clustering strategy. In this work, we focus on the latter part of this mutually beneficial relationship. To this end, we introduce Deep Goal-Oriented Clustering (DGC), a probabilistic framework that clusters the data by jointly using supervision via side-information and unsupervised modeling of the inherent data structure in an end-to-end fashion. We show the effectiveness of our model on a range of datasets by achieving prediction accuracies comparable to the state-of-the-art, while, more importantly in our setting, simultaneously learning congruent clustering strategies.

The production of lithium-ion battery cells is characterized by a high degree of complexity due to numerous cause-effect relationships between process characteristics. Knowledge about the multi-stage production is spread among several experts, rendering tasks as failure analysis challenging. In this paper, a new method is presented that includes expert knowledge acquisition in production ramp-up by combining Failure Mode and Effects Analysis (FMEA) with a Bayesian Network. Special algorithms are presented that help detect and resolve inconsistencies between the expert-provided parameters which are bound to occur when collecting knowledge from several process experts. We show the effectiveness of this holistic method by building up a large scale, cross-process Bayesian Failure Network in lithium-ion battery production and its application for root cause analysis.

The land cover classification has played an important role in remote sensing because it can intelligently identify things in one huge remote sensing image to reduce the work of humans. However, a lot of classification methods are designed based on the pixel feature or limited spatial feature of the remote sensing image, which limits the classification accuracy and universality of their methods. This paper proposed a novel method to take into the information of remote sensing image, i.e., geographic latitude-longitude information. In addition, a dual-branch convolutional neural network (CNN) classification method is designed in combination with the global information to mine the pixel features of the image. Then, the features of the two neural networks are fused with another fully neural network to realize the classification of remote sensing images. Finally, two remote sensing images are used to verify the effectiveness of our method, including hyperspectral imaging (HSI) and polarimetric synthetic aperture radar (PolSAR) imagery. The result of the proposed method is superior to the traditional single-channel convolutional neural network.

This paper analyzes the convergence for a large class of Riemannian stochastic approximation (SA) schemes, which aim at tackling stochastic optimization problems. In particular, the recursions we study use either the exponential map of the considered manifold (geodesic schemes) or more general retraction functions (retraction schemes) used as a proxy for the exponential map. Such approximations are of great interest since they are low complexity alternatives to geodesic schemes. Under the assumption that the mean field of the SA is correlated with the gradient of a smooth Lyapunov function (possibly non-convex), we show that the above Riemannian SA schemes find an ${\mathcal{O}}(b_\infty + \log n / \sqrt{n})$-stationary point (in expectation) within ${\mathcal{O}}(n)$ iterations, where $b_\infty \geq 0$ is the asymptotic bias. Compared to previous works, the conditions we derive are considerably milder. First, all our analysis are global as we do not assume iterates to be a-priori bounded. Second, we study biased SA schemes. To be more specific, we consider the case where the mean-field function can only be estimated up to a small bias, and/or the case in which the samples are drawn from a controlled Markov chain. Third, the conditions on retractions required to ensure convergence of the related SA schemes are weak and hold for well-known examples. We illustrate our results on three machine learning problems.