We consider the problem of learning a low dimensional representation for compositional data. Compositional data consists of a collection of nonnegative data that sum to a constant value. Since the parts of the collection are statistically dependent, many standard tools cannot be directly applied. Instead, compositional data must be first transformed before analysis. Focusing on principal component analysis (PCA), we propose an approach that allows low dimensional representation learning directly from the original data.

In this paper, we present an approach for doing so. Given a demonstration of a path, a first network generates an abstraction of the path. Equipped with this abstraction, a second network then observes the world and decides how to act in order to retrace the path under noisy actuation and a changing environment. The two networks are optimized end-to-end at training time. We evaluate the method in two realistic simulators, performing path following both forwards and backwards. Our experiments show that our approach outperforms both a classical approach to solving this task as well as a number of other baselines.

We present a new approach to the problems of evaluating and learning personalized decision policies from observational data of past contexts, decisions, and outcomes. Only the outcome of the enacted decision is available and the historical policy is unknown. These problems arise in personalized medicine using electronic health records and in internet advertising. Existing approaches use inverse propensity weighting (or, doubly robust versions) to make historical outcome (or, residual) data look like it were generated by a new policy being evaluated or learned. But this relies on a plug-in approach that rejects data points with a decision that disagrees with the new policy, leading to high variance estimates and ineffective learning. We propose a new, balance-based approach that too makes the data look like the new policy but does so directly by finding weights that optimize for balance between the weighted data and the target policy in the given, finite sample, which is equivalent to minimizing worst-case or posterior conditional mean square error.

Sum-product networks have recently emerged as an attractive representation due to their dual view as a special type of deep neural network with clear semantics and a special type of probabilistic graphical model for which inference is always tractable. Those properties follow from some conditions (i.e., completeness and decomposability) that must be respected by the structure of the network. As a result, it is not easy to specify a valid sum-product network by hand and therefore structure learning techniques are typically used in practice. This paper describes a new online structure learning technique for feed-forward and recurrent SPNs. The algorithm is demonstrated on real-world datasets with continuous features for which it is not clear what network architecture might be best, including sequence datasets of varying length.

Interactive partially observable Markov decision processes (I-POMDPs) provide a principled framework for planning and acting in a partially observable, stochastic and multi-agent environment. It extends POMDPs to multi-agent settings by including models of other agents in the state space and forming a hierarchical belief structure. In order to predict other agents' actions using I-POMDPs, we propose an approach that effectively uses Bayesian inference and sequential Monte Carlo sampling to learn others' intentional models which ascribe to them beliefs, preferences and rationality in action selection. Empirical results show that our algorithm accurately learns models of the other agent and has superior performance than methods that use subintentional models. Our approach serves as a generalized Bayesian learning algorithm that learns other agents' beliefs, strategy levels, and transition, observation and reward functions.

In this paper, we consider online F-measure optimization (OFO). Unlike traditional performance metrics (e.g., classification error rate), F-measure is non-decomposable over training examples and is a non-convex function of model parameters, making it much more difficult to be optimized in an online fashion. Most existing results of OFO usually suffer from high memory/computational costs and/or lack statistical consistency guarantee for optimizing F-measure at the population level. To advance OFO, we propose an efficient online algorithm based on simultaneously learning a posterior probability of class and learning an optimal threshold by minimizing a stochastic strongly convex function with unknown strong convexity parameter. A key component of the proposed method is a novel stochastic algorithm with low memory and computational costs, which can enjoy a convergence rate of $\widetilde O(1/\sqrt{n})$ for learning the optimal threshold under a mild condition on the convergence of the posterior probability, where $n$ is the number of processed examples. It is provably faster than its predecessor based on a heuristic for updating the threshold. The experiments verify the efficiency of the proposed algorithm in comparison with state-of-the-art OFO algorithms.

The problem is undecidable and even practical instances are challenging. Inspired by how human experts construct loop invariants, we propose a reasoning framework Code2Inv that constructs the solution by multi-step decision making and querying an external program graph memory block. By training with reinforcement learning, Code2Inv captures rich program features and avoids the need for ground truth solutions as supervision. Compared to previous learning tasks in domains with graph-structured data, it addresses unique challenges, such as a binary objective function and an extremely sparse reward that is given by an automated theorem prover only after the complete loop invariant is proposed. We evaluate Code2Inv on a suite of 133 benchmark problems and compare it to three state-of-the-art systems. It solves 106 problems compared to 73 by a stochastic search-based system, 77 by a heuristic search-based system, and 100 by a decision tree learning-based system. Moreover, the strategy learned can be generalized to new programs: compared to solving new instances from scratch, the pre-trained agent is more sample efficient in finding solutions.

While recent developments in autonomous vehicle (AV) technology highlight substantial progress, we lack tools for rigorous and scalable testing. Real-world testing, the de facto evaluation environment, places the public in danger, and, due to the rare nature of accidents, will require billions of miles in order to statistically validate performance claims. We implement a simulation framework that can test an entire modern autonomous driving system, including, in particular, systems that employ deep-learning perception and control algorithms. Using adaptive importance-sampling methods to accelerate rare-event probability evaluation, we estimate the probability of an accident under a base distribution governing standard traffic behavior. We demonstrate our framework on a highway scenario, accelerating system evaluation by 2-20 times over naive Monte Carlo sampling methods and 10-300P times (where P is the number of processors) over real-world testing.

Complex numbers have long been favoured for digital signal processing, yet complex representations rarely appear in deep learning architectures. RNNs, widely used to process time series and sequence information, could greatly benefit from complex representations. We present a novel complex gated recurrent cell, which is a hybrid cell combining complex-valued and norm-preserving state transitions with a gating mechanism. The resulting RNN exhibits excellent stability and convergence properties and performs competitively on the synthetic memory and adding task, as well as on the real-world tasks of human motion prediction.

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.