In this study, importance of user inputs is studied in the context of personalizing human activity recognition models using incremental learning. Inertial sensor data from three body positions are used, and the classification is based on Learn++ ensemble method. Three different approaches to update models are compared: non-supervised, semi-supervised and supervised. Non-supervised approach relies fully on predicted labels, supervised fully on user labeled data, and the proposed method for semi-supervised learning, is a combination of these two. In fact, our experiments show that by relying on predicted labels with high confidence, and asking the user to label only uncertain observations (from 12% to 26% of the observations depending on the used base classifier), almost as low error rates can be achieved as by using supervised approach. In fact, the difference was less than 2%-units. Moreover, unlike non-supervised approach, semi-supervised approach does not suffer from drastic concept drift, and thus, the error rate of the non-supervised approach is over 5%-units higher than using semi-supervised approach.

The information-theoretic analysis by Russo and Van Roy (2014) in combination with minimax duality has proved a powerful tool for the analysis of online learning algorithms in full and partial information settings. In most applications there is a tantalising similarity to the classical analysis based on mirror descent. We make a formal connection, showing that the information-theoretic bounds in most applications can be derived from existing techniques for online convex optimisation. Besides this, for $k$-armed adversarial bandits we provide an efficient algorithm with regret that matches the best information-theoretic upper bound and improve best known regret guarantees for online linear optimisation on $\ell_p$-balls and bandits with graph feedback.

We give a formal and complete characterization of the explicit regularizer induced by dropout in deep linear networks with squared loss. We show that (a) the explicit regularizer is composed of an $\ell_2$-path regularizer and other terms that are also re-scaling invariant, (b) the convex envelope of the induced regularizer is the squared nuclear norm of the network map, and (c) for a sufficiently large dropout rate, we characterize the global optima of the dropout objective. We validate our theoretical findings with empirical results.

Hashing has been widely adopted for large-scale data retrieval in many domains, due to its low storage cost and high retrieval speed. Existing cross-modal hashing methods optimistically assume that the correspondence between training samples across modalities are readily available. This assumption is unrealistic in practical applications. In addition, these methods generally require the same number of samples across different modalities, which restricts their flexibility. We propose a flexible cross-modal hashing approach (Flex-CMH) to learn effective hashing codes from weakly-paired data, whose correspondence across modalities are partially (or even totally) unknown. FlexCMH first introduces a clustering-based matching strategy to explore the local structure of each cluster, and thus to find the potential correspondence between clusters (and samples therein) across modalities. To reduce the impact of an incomplete correspondence, it jointly optimizes in a unified objective function the potential correspondence, the cross-modal hashing functions derived from the correspondence, and a hashing quantitative loss. An alternative optimization technique is also proposed to coordinate the correspondence and hash functions, and to reinforce the reciprocal effects of the two objectives. Experiments on publicly multi-modal datasets show that FlexCMH achieves significantly better results than state-of-the-art methods, and it indeed offers a high degree of flexibility for practical cross-modal hashing tasks.

Online Normalization is a new technique for normalizing the hidden activations of a neural network. Like Batch Normalization, it normalizes the sample dimension. While Online Normalization does not use batches, it is as accurate as Batch Normalization. We resolve a theoretical limitation of Batch Normalization by introducing an unbiased technique for computing the gradient of normalized activations. Online Normalization works with automatic differentiation by adding statistical normalization as a primitive. This technique can be used in cases not covered by some other normalizers, such as recurrent networks, fully connected networks, and networks with activation memory requirements prohibitive for batching. We show its applications to image classification, image segmentation, and language modeling. We present formal proofs and experimental results on ImageNet, CIFAR, and PTB datasets.

In this effort we propose a novel approach for reconstructing multivariate functions from training data, by identifying both a suitable network architecture and an initialization using polynomial-based approximations. Training deep neural networks using gradient descent can be interpreted as moving the set of network parameters along the loss landscape in order to minimize the loss functional. The initialization of parameters is important for iterative training methods based on descent. Our procedure produces a network whose initial state is a polynomial representation of the training data. The major advantage of this technique is from this initialized state the network may be improved using standard training procedures. Since the network already approximates the data, training is more likely to produce a set of parameters associated with a desirable local minimum. We provide the details of the theory necessary for constructing such networks and also consider several numerical examples that reveal our approach ultimately produces networks which can be effectively trained from our initialized state to achieve an improved approximation for a large class of target functions.

Learning by demonstration is a versatile and rapid mechanism for transferring motor skills from a teacher to a learner. A particular challenge in imitation learning is the so-called correspondence problem, which involves mapping actions between a teacher and a learner having substantially different embodiments (say, human to robot). We present a general, model free and non-parametric imitation learning algorithm based on regression between two Hilbert spaces. We accomplish this via Kirszbraun's extension theorem --- apparently the first application of this technique to supervised learning --- and analyze its statistical and computational aspects. We begin by formulating the correspondence problem in terms of quadratically constrained quadratic program (QCQP) regression. Then we describe a procedure for smoothing the training data, which amounts to regularizing hypothesis complexity via its Lipschitz constant. The Lipschitz constant is tuned via a Structural Risk Minimization (SRM) procedure, based on the covering-number risk bounds we derive. We apply our technique to a static posture imitation task between two robotic manipulators with different embodiments, and report promising results.

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set filtrations and distance-bases filtrations. We present three novel applications: the topological layer can (i) serve as a regularizer directly on data or the weights of machine learning models, (ii) construct a loss on the output of a deep generative network to incorporate topological priors, and (iii) perform topological adversarial attacks on deep networks trained with persistence features. The code is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications.

We consider a new family of operators for reinforcement learning with the goal of alleviating the negative effects and becoming more robust to approximation or estimation errors. Various theoretical results are established, which include showing on a sample path basis that our family of operators preserve optimality and increase the action gap. Our empirical results illustrate the strong benefits of our family of operators, significantly outperforming the classical Bellman operator and recently proposed operators.

Behavioral cloning reduces policy learning to supervised learning by training a discriminative model to predict expert actions given observations. Such discriminative models are non-causal: the training procedure is unaware of the causal structure of the interaction between the expert and the environment. We point out that ignoring causality is particularly damaging because of the distributional shift in imitation learning. In particular, it leads to a counter-intuitive "causal confusion" phenomenon: access to more information can yield worse performance. We investigate how this problem arises, and propose a solution to combat it through targeted interventions---either environment interaction or expert queries---to determine the correct causal model. We show that causal confusion occurs in several benchmark control domains as well as realistic driving settings, and validate our solution against DAgger and other baselines and ablations.