Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we train near-term quantum circuits to classify data represented by non-orthogonal quantum probability distributions using the Adam stochastic optimization algorithm. This is achieved by iterative interactions of a classical device with a quantum processor to discover the parameters of an unknown non-unitary quantum circuit. This circuit learns to simulates the unknown structure of a generalized quantum measurement, or Positive-Operator-Value-Measure (POVM), that is required to optimally distinguish possible distributions of quantum inputs. Notably we use universal circuit topologies, with a theoretically motivated circuit design, which guarantees that our circuits can in principle learn to perform arbitrary input-output mappings. Our numerical simulations show that shallow quantum circuits could be trained to discriminate among various pure and mixed quantum states exhibiting a trade-off between minimizing erroneous and inconclusive outcomes with comparable performance to theoretically optimal POVMs. We train the circuit on different classes of quantum data and evaluate the generalization error on unseen mixed quantum states. This generalization power hence distinguishes our work from standard circuit optimization and provides an example of quantum machine learning for a task that has inherently no classical analogue.

Effective game-theoretic modeling of defender-attacker behavior is becoming increasingly important. In many domains, the defender functions not only as a player but also the designer of the game's payoff structure. We study Stackelberg Security Games where the defender, in addition to allocating defensive resources to protect targets from the attacker, can strategically manipulate the attacker's payoff under budget constraints in weighted L^p-norm form regarding the amount of change. Focusing on problems with weighted L^1-norm form constraint, we present (i) a mixed integer linear program-based algorithm with approximation guarantee; (ii) a branch-and-bound based algorithm with improved efficiency achieved by effective pruning; (iii) a polynomial time approximation scheme for a special but practical class of problems. In addition, we show that problems under budget constraints in L^0-norm form and weighted L^\infty-norm form can be solved in polynomial time. We provide an extensive experimental evaluation of our proposed algorithms.

This paper presents the Crossmodal Attentive Skill Learner (CASL), integrated with the recently-introduced Asynchronous Advantage Option-Critic (A2OC) architecture [Harb et al., 2017] to enable hierarchical reinforcement learning across multiple sensory inputs. We provide concrete examples where the approach not only improves performance in a single task, but accelerates transfer to new tasks. We demonstrate the attention mechanism anticipates and identifies useful latent features, while filtering irrelevant sensor modalities during execution. We modify the Arcade Learning Environment [Bellemare et al., 2013] to support audio queries, and conduct evaluations of crossmodal learning in the Atari 2600 game Amidar. Finally, building on the recent work of Babaeizadeh et al. [2017], we open-source a fast hybrid CPU-GPU implementation of CASL.

In programming by example, users "write" programs by generating a small number of input-output examples and asking the computer to synthesize consistent programs. We consider an unsolved problem in this domain: learning regular expressions (regexes) from positive and negative example strings. This problem is challenging, as (1) user-generated examples may not be informative enough to sufficiently constrain the hypothesis space, and (2) even if user-generated examples are in principle informative, there is still a massive search space to examine. We frame regex induction as the problem of inferring a probabilistic regular grammar and propose an efficient inference approach that uses a novel stochastic process recognition model. This model incrementally "grows" a grammar using positive examples as a scaffold. We show that this approach is competitive with human ability to learn regexes from examples.

This paper describes and motivates a new decision theory known as functional decision theory (FDT), as distinct from causal decision theory and evidential decision theory. Functional decision theorists hold that the normative principle for action is to treat one's decision as the output of a fixed mathematical function that answers the question, "Which output of this very function would yield the best outcome?" Adhering to this principle delivers a number of benefits, including the ability to maximize wealth in an array of traditional decision-theoretic and game-theoretic problems where CDT and EDT perform poorly. Using one simple and coherent decision rule, functional decision theorists (for example) achieve more utility than CDT on Newcomb's problem, more utility than EDT on the smoking lesion problem, and more utility than both in Parfit's hitchhiker problem. In this paper, we define FDT, explore its prescriptions in a number of different decision problems, compare it to CDT and EDT, and give philosophical justifications for FDT as a normative theory of decision-making.

Unsupervised learning is widely recognized as one of the most important challenges facing machine learning nowa- days. However, in spite of hundreds of papers on the topic being published every year, current theoretical understanding and practical implementations of such tasks, in particular of clustering, is very rudimentary. This note focuses on clustering. I claim that the most signif- icant challenge for clustering is model selection. In contrast with other common computational tasks, for clustering, dif- ferent algorithms often yield drastically different outcomes. Therefore, the choice of a clustering algorithm, and their pa- rameters (like the number of clusters) may play a crucial role in the usefulness of an output clustering solution. However, currently there exists no methodical guidance for clustering tool-selection for a given clustering task. Practitioners pick the algorithms they use without awareness to the implications of their choices and the vast majority of theory of clustering papers focus on providing savings to the resources needed to solve optimization problems that arise from picking some concrete clustering objective. Saving that pale in com- parison to the costs of mismatch between those objectives and the intended use of clustering results. I argue the severity of this problem and describe some recent proposals aiming to address this crucial lacuna.

Machine learning has witnessed the tremendous success of solving tasks depending on a hyperparameter. While multi-task learning is celebrated for its capacity to solve jointly a finite number of tasks, learning a continuum of tasks for various loss functions is still a challenge. A promising approach, called Parametric Task Learning, has paved the way in the case of piecewise-linear loss functions. We propose a generic approach, called Infinite Task Learning, to solve jointly a continuum of tasks via Vector-Valued Reproducing Kernel Hilbert Spaces. We provide generalization guarantees to the suggested scheme and illustrate its efficiency in cost-sensitive classification, quantile regression and density level set estimation.

Traditional literature on pattern recognition and neural networks utilizes the linear Perceptron, a multiply-accumulate architecture fed into an (optional) activation function introduced by Rosenblatt [40], as the building block of a multitude of complex architectures modelling neural computation. In recent years, multilayered, complex architectures of neural networks have enjoyed an unprecedented growth in popularity, with the introduction of the paradigm of deep learning [4]. An illustrative example of the power of deep learning is Convolutional Neural Networks; although they were the state of the art when they were introduced, two decades ago [24], it wasn't until recently that they were systematically applied to image recognition challenges[23], achieving results comparable to humans (e.g.

In recent years, the Word2Vec model trained with the Negative Sampling loss function has shown state-of-the-art results in a number of machine learning tasks, including language modeling tasks, such as word analogy and word similarity, and in recommendation tasks, through Prod2Vec, an extension that applies to modeling user shopping activity and user preferences. Several methods that aim to improve upon the standard Negative Sampling loss have been proposed. In our paper we pursue more sophisticated Negative Sampling, by leveraging ideas from the field of Generative Adversarial Networks (GANs), and propose Adversarial Negative Sampling. We build upon the recent progress made in stabilizing the training objective of GANs in the discrete data setting, and introduce a new GAN-Word2Vec model. We evaluate our model on the task of basket completion, and show significant improvements in performance over Word2Vec trained using standard loss functions, including Noise Contrastive Estimation and Negative Sampling.

CBL U Cambridge, UK Nonlinear ICA is a fundamental problem for unsupervised representation learning, emphasizing the capacity to recover the underlying latent variables generating the data (i.e., identifiability). Recently, the very first identifiability proofs for nonlinear ICA have been proposed, leveraging the temporal structure of the independent components. Here, we propose a general framework for nonlinear ICA, which, as a special case, can make use of temporal structure. It is based on augmenting the data by an auxiliary variable, such as the time index, the history of the time series, or any other available information. We propose to learn nonlinear ICA by discriminating between true augmented data, or data in which the auxiliary variable has been randomized. This enables the framework to be implemented algorithmically through logistic regression, possibly in a neural network. We provide a comprehensive proof of the identifiability of the model as well as the consistency of our estimation method. The approach not only provides a general theoretical framework combining and generalizing previously proposed nonlinear ICA models and algorithms, but also brings practical advantages.