Frequency-specific patterns of neural activity are traditionally interpreted as sustained rhythmic oscillations, and related to cognitive mechanisms such as attention, high level visual processing or motor control. While alpha waves (8--12\,Hz) are known to closely resemble short sinusoids, and thus are revealed by Fourier analysis or wavelet transforms, there is an evolving debate that electromagnetic neural signals are composed of more complex waveforms that cannot be analyzed by linear filters and traditional signal representations. In this paper, we propose to learn dedicated representations of such recordings using a multivariate convolutional sparse coding (CSC) algorithm. Applied to electroencephalography (EEG) or magnetoencephalography (MEG) data, this method is able to learn not only prototypical temporal waveforms, but also associated spatial patterns so their origin can be localized in the brain. Our algorithm is based on alternated minimization and a greedy coordinate descent solver that leads to state-of-the-art running time on long time series. To demonstrate the implications of this method, we apply it to MEG data and show that it is able to recover biological artifacts. More remarkably, our approach also reveals the presence of non-sinusoidal mu-shaped patterns, along with their topographic maps related to the somatosensory cortex.

Recent work in theoretical neuroscience has shown that information-theoretic efficient neural codes, which allocate neural resources to maximize the mutual information between stimuli and neural responses, give rise to a lawful relationship between perceptual bias and discriminability that is observed across a wide variety of psychophysical tasks in human observers (Wei & Stocker 2017). Here we generalize these results to show that the same law arises under a much larger family of optimal neural codes, introducing a unifying framework that we call power-law efficient coding. Specifically, we show that the same lawful relationship between bias and discriminability arises whenever Fisher information is allocated proportional to any power of the prior distribution. This family includes neural codes that are optimal for minimizing Lp error for any p, indicating that the lawful relationship observed in human psychophysical data does not require information-theoretically optimal neural codes. Furthermore, we derive the exact constant of proportionality governing the relationship between bias and discriminability for different power laws (which includes information-theoretically optimal codes, where the power is 2, and so-called discrimax codes, where power is 1/2), and different choices of optimal decoder. As a bonus, our framework provides new insights into anti-Bayesian perceptual biases, in which percepts are biased away from the center of mass of the prior. We derive an explicit formula that clarifies precisely which combinations of neural encoder and decoder can give rise to such biases.

Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training data faces severe challenges, including: (i) scarcity of training data; (ii) need for plausible reconstructions that are physically feasible; (iii) need for fast reconstruction, especially in real-time applications. We develop a successful system solving all these challenges, using as basic architecture the repetitive application of alternating proximal and data fidelity constraints. We learn a proximal map that works well with real images based on residual networks with recurrent blocks. Extensive experiments are carried out under different settings: (a) reconstructing abdominal MRI of pediatric patients from highly undersampled k-space data and (b) super-resolving natural face images. Our key findings include: 1. a recurrent ResNet with a single residual block (10-fold repetition) yields an effective proximal which accurately reveals MR image details. 2. Our architecture significantly outperforms conventional non-recurrent deep ResNets by 2dB SNR; it is also trained much more rapidly.

Deep neural networks have been known to be vulnerable to adversarial attacks, raising lots of security concerns in the practical deployment. Popular defensive approaches can be formulated as a (distributionally) robust optimization problem, which minimizes a ``point estimate'' of worst-case loss derived from either per-datum perturbation or adversary data-generating distribution within certain pre-defined constraints. This point estimate ignores potential test adversaries that are beyond the pre-defined constraints. The model robustness might deteriorate sharply in the scenario of stronger test adversarial data. In this work, a novel robust training framework is proposed to alleviate this issue, Bayesian Robust Learning, in which a distribution is put on the adversarial data-generating distribution to account for the uncertainty of the adversarial data-generating process.

Electronic health records provide a rich source of data for machine learning methods to learn dynamic treatment responses over time. However, any direct estimation is hampered by the presence of time-dependent confounding, where actions taken are dependent on time-varying variables related to the outcome of interest. Drawing inspiration from marginal structural models, a class of methods in epidemiology which use propensity weighting to adjust for time-dependent confounders, we introduce the Recurrent Marginal Structural Network - a sequence-to-sequence architecture for forecasting a patient's expected response to a series of planned treatments.

Recent progress in deep learning for audio synthesis opens the way to models that directly produce the waveform, shifting away from the traditional paradigm of relying on vocoders or MIDI synthesizers for speech or music generation. Despite their successes, current state-of-the-art neural audio synthesizers such as WaveNet and SampleRNN suffer from prohibitive training and inference times because they are based on autoregressive models that generate audio samples one at a time at a rate of 16kHz. In this work, we study the more computationally efficient alternative of generating the waveform frame-by-frame with large strides. We present a lightweight neural audio synthesizer for the original task of generating musical notes given desired instrument, pitch and velocity. Our model is trained end-to-end to generate notes from nearly 1000 instruments with a single decoder, thanks to a new loss function that minimizes the distances between the log spectrograms of the generated and target waveforms. On the generalization task of synthesizing notes for pairs of pitch and instrument not seen during training, SING produces audio with significantly improved perceptual quality compared to a state-of-the-art autoencoder based on WaveNet as measured by a Mean Opinion Score (MOS), and is about 32 times faster for training and 2, 500 times faster for inference.

In many sequential decision making tasks, it is challenging to design reward functions that help an RL agent efficiently learn behavior that is considered good by the agent designer. A number of different formulations of the reward-design problem, or close variants thereof, have been proposed in the literature. In this paper we build on the Optimal Rewards Framework of Singh et al. that defines the optimal intrinsic reward function as one that when used by an RL agent achieves behavior that optimizes the task-specifying or extrinsic reward function. Previous work in this framework has shown how good intrinsic reward functions can be learned for lookahead search based planning agents. Whether it is possible to learn intrinsic reward functions for learning agents remains an open problem. In this paper we derive a novel algorithm for learning intrinsic rewards for policy-gradient based learning agents. We compare the performance of an augmented agent that uses our algorithm to provide additive intrinsic rewards to an A2C-based policy learner (for Atari games) and a PPO-based policy learner (for Mujoco domains) with a baseline agent that uses the same policy learners but with only extrinsic rewards. Our results show improved performance on most but not all of the domains.

We consider the problem of online learning in the linear contextual bandits setting, but in which there are also strong individual fairness constraints governed by an unknown similarity metric. These constraints demand that we select similar actions or individuals with approximately equal probability DHPRZ12, which may be at odds with optimizing reward, thus modeling settings where profit and social policy are in tension. We assume we learn about an unknown Mahalanobis similarity metric from only weak feedback that identifies fairness violations, but does not quantify their extent. This is intended to represent the interventions of a regulator who knows unfairness when he sees it but nevertheless cannot enunciate a quantitative fairness metric over individuals. Our main result is an algorithm in the adversarial context setting that has a number of fairness violations that depends only logarithmically on T, while obtaining an optimal O(sqrt(T)) regret bound to the best fair policy.

Despite their impressive performance, Deep Neural Networks (DNNs) typically underperform Gradient Boosting Trees (GBTs) on many tabular-dataset learning tasks. We propose that applying a different regularization coefficient to each weight might boost the performance of DNNs by allowing them to make more use of the more relevant inputs. However, this will lead to an intractable number of hyperparameters. Here, we introduce Regularization Learning Networks (RLNs), which overcome this challenge by introducing an efficient hyperparameter tuning scheme which minimizes a new Counterfactual Loss. Our results show that RLNs significantly improve DNNs on tabular datasets, and achieve comparable results to GBTs, with the best performance achieved with an ensemble that combines GBTs and RLNs. RLNs produce extremely sparse networks, eliminating up to 99.8% of the network edges and 82% of the input features, thus providing more interpretable models and reveal the importance that the network assigns to different inputs. RLNs could efficiently learn a single network in datasets that comprise both tabular and unstructured data, such as in the setting of medical imaging accompanied by electronic health records.

Risk management in dynamic decision problems is a primary concern in many fields, including financial investment, autonomous driving, and healthcare. The mean-variance function is one of the most widely used objective functions in risk management due to its simplicity and interpretability. Existing algorithms for mean-variance optimization are based on multi-time-scale stochastic approximation, whose learning rate schedules are often hard to tune, and have only asymptotic convergence proof. In this paper, we develop a model-free policy search framework for mean-variance optimization with finite-sample error bound analysis (to local optima). Our starting point is a reformulation of the original mean-variance function with its Fenchel dual, from which we propose a stochastic block coordinate ascent policy search algorithm. Both the asymptotic convergence guarantee of the last iteration's solution and the convergence rate of the randomly picked solution are provided, and their applicability is demonstrated on several benchmark domains.