As application demands for online convex optimization accelerate, the need for designing new methods that simultaneously cover a large class of convex functions and impose the lowest possible regret is highly rising. Known online optimization methods usually perform well only in specific settings, and their performance depends highly on the geometry of the decision space and cost functions. However, in practice, lack of such geometric information leads to confusion in using the appropriate algorithm. To address this issue, some adaptive methods have been proposed that focus on adaptively learning parameters such as step size, Lipschitz constant, and strong convexity coefficient, or on specific parametric families such as quadratic regularizers. In this work, we generalize these methods and propose a framework that competes with the best algorithm in a family of expert algorithms. Our framework includes many of the well-known adaptive methods including MetaGrad, MetaGrad+C, and Ader. We also introduce a second algorithm that computationally outperforms our first algorithm with at most a constant factor increase in regret. Finally, as a representative application of our proposed algorithm, we study the problem of learning the best regularizer from a family of regularizers for Online Mirror Descent. Empirically, we support our theoretical findings in the problem of learning the best regularizer on the simplex and $l_2$-ball in a multiclass learning problem.

We present a weakly-supervised data augmentation approach to improve Named Entity Recognition (NER) in a challenging domain: extracting biomedical entities (e.g., proteins) from the scientific literature. First, we train a neural NER (NNER) model over a small seed of fully-labeled examples. Second, we use a reference set of entity names (e.g., proteins in UniProt) to identify entity mentions with high precision, but low recall, on an unlabeled corpus. Third, we use the NNER model to assign weak labels to the corpus. Finally, we retrain our NNER model iteratively over the augmented training set, including the seed, the reference-set examples, and the weakly-labeled examples, which improves model performance. We show empirically that this augmented bootstrapping process significantly improves NER performance, and discuss the factors impacting the efficacy of the approach.

Non-stationarity appears in many online applications such as web search and advertising. In this paper, we study the online learning to rank problem in a non-stationary environment where user preferences change abruptly at an unknown moment in time. We consider the problem of identifying the K most attractive items and propose cascading non-stationary bandits, an online learning variant of the cascading model, where a user browses a ranked list from top to bottom and clicks on the first attractive item. We propose two algorithms for solving this non-stationary problem: CascadeDUCB and CascadeSWUCB. We analyze their performance and derive gap-dependent upper bounds on the n-step regret of these algorithms. We also establish a lower bound on the regret for cascading non-stationary bandits and show that both algorithms match the lower bound up to a logarithmic factor. Finally, we evaluate their performance on a real-world web search click dataset.

This paper is concerned with the robustness of VAEs to adversarial attacks. We highlight that conventional VAEs are brittle under attack but that methods recently introduced for disentanglement such as $\beta$-TCVAE (Chen et al., 2018) improve robustness, as demonstrated through a variety of previously proposed adversarial attacks (Tabacof et al. (2016); Gondim-Ribeiro et al. (2018); Kos et al.(2018)). This motivated us to develop Seatbelt-VAE, a new hierarchical disentangled VAE that is designed to be significantly more robust to adversarial attacks than existing approaches, while retaining high quality reconstructions.

There have been different strategies to improve the performance of a machine learning model, e.g., increasing the depth, width, and/or nonlinearity of the model, and using ensemble learning to aggregate multiple base/weak learners in parallel or in series. This paper proposes a novel strategy called patch learning (PL) for this problem. It consists of three steps: 1) train an initial global model using all training data; 2) identify from the initial global model the patches which contribute the most to the learning error, and train a (local) patch model for each such patch; and, 3) update the global model using training data that do not fall into any patch. To use a PL model, we first determine if the input falls into any patch. If yes, then the corresponding patch model is used to compute the output. Otherwise, the global model is used. We explain in detail how PL can be implemented using fuzzy systems. Five regression problems on 1D/2D/3D curve fitting, nonlinear system identification, and chaotic time-series prediction, verified its effectiveness. To our knowledge, the PL idea has not appeared in the literature before, and it opens up a promising new line of research in machine learning.

This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection directions, properties of the projection matrix, reconstruction error minimization, and we connect to auto-encoder. Then, PCA with singular value decomposition, dual PCA, and kernel PCA are covered. SPCA using both scoring and Hilbert-Schmidt independence criterion are explained. Kernel SPCA using both direct and dual approaches are then introduced. We cover all cases of projection and reconstruction of training and out-of-sample data. Finally, some simulations are provided on Frey and AT&T face datasets for verifying the theory in practice.

Motion planning is an essential component in most of today's robotic applications. In this work, we consider the learning setting, where a set of solved motion planning problems is used to improve the efficiency of motion planning on different, yet similar problems. This setting is important in applications with rapidly changing environments such as in e-commerce, among others. We investigate a general deep learning based approach, where a neural network is trained to map an image of the domain, the current robot state, and a goal robot state to the next robot state in the plan. We focus on the learning algorithm, and compare supervised learning methods with reinforcement learning (RL) algorithms. We first establish that supervised learning approaches are inferior in their accuracy due to insufficient data on the boundary of the obstacles, an issue that RL methods mitigate by actively exploring the domain. We then propose a modification of the popular DDPG RL algorithm that is tailored to motion planning domains, by exploiting the known model in the problem and the set of solved plans in the data. We show that our algorithm, dubbed DDPG-MP, significantly improves the accuracy of the learned motion planning policy. Finally, we show that given enough training data, our method can plan significantly faster on novel domains than off-the-shelf sampling based motion planners. Results of our experiments are shown in https://youtu.be/wHQ4Y4mBRb8.

Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss the capabilities and limitations of TAEs through both theoretical and numerical analyses. Theoretically, we derive bounds for nonlinear TAE performance in slow mode discovery and show that in general TAEs learn a mixture of slow and maximum variance modes. Numerically, we illustrate cases where TAEs can and cannot correctly identify the leading slowest mode in two example systems: a 2D "Washington beltway" potential and the alanine dipeptide molecule in explicit water. We also compare the TAE results with those obtained using state-free reversible VAMPnets (SRVs) as a variational-based neural network approach for slow modes discovery, and show that SRVs can correctly discover slow modes where TAEs fail.

We consider the problem of training a model under the presence of label noise. Current approaches identify samples with potentially incorrect labels and reduce their influence on the learning process by either assigning lower weights to them or completely removing them from the training set. In the first case the model however still learns from noisy labels; in the latter approach, good training data can be lost. In this paper, we propose an iterative semi-supervised mechanism for robust learning which excludes noisy labels but is still able to learn from the corresponding samples. To this end, we add an unsupervised loss term that also serves as a regularizer against the remaining label noise. We evaluate our approach on common classification tasks with different noise ratios. Our robust models outperform the state-of-the-art methods by a large margin. Especially for very large noise ratios, we achieve up to 20 % absolute improvement compared to the previous best model.

Instrumental variable regression is a strategy for learning causal relationships in observational data. If measurements of input X and output Y are confounded, the causal relationship can nonetheless be identified if an instrumental variable Z is available that influences X directly, but is conditionally independent of Y given X. The classic two-stage least squares algorithm (2SLS) simplifies the estimation problem by modeling all relationships as linear functions. We propose kernel instrumental variable regression (KIV), a nonparametric generalization of 2SLS, modeling relations among X, Y, and Z as nonlinear functions in reproducing kernel Hilbert spaces (RKHSs). We prove the consistency of KIV under mild assumptions, and derive conditions under which the convergence rate achieves the minimax optimal rate for unconfounded, one-stage RKHS regression. In doing so, we obtain an efficient ratio between training sample sizes used in the algorithm's first and second stages. In experiments, KIV outperforms state of the art alternatives for nonparametric instrumental variable regression.