Over the past few years, the multi-armed bandit model has become increasingly popular in the machine learning community, partly because of applications including online content optimization. This paper reviews two different sequential learning tasks that have been considered in the bandit literature ; they can be formulated as (sequentially) learning which distribution has the highest mean among a set of distributions, with some constraints on the learning process. For both of them (regret minimization and best arm identification) we present recent, asymptotically optimal algorithms. We compare the behaviors of the sampling rule of each algorithm as well as the complexity terms associated to each problem.

We first removed irrelevant tweets. A step we were able to take thanks to our "Small Data" situation. We then used Jeremy Singer-Vine's markovify -- a Markov chains implementation -- to model Netanyahu's original tweets. That alone actually gave us a pretty good baseline, in a very short time. We also expanded the Markov model to obey sentence structure using spaCy, a part-of-speech tagger.

Duan 1,2 1 Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, PR China 2 Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer [1-3]. Machine learning represents an important field with broad applications where quantum computer may offer significant speedup [4-8]. Several quantum algorithms for discriminative machine learning [9] have been found based on efficient solving of linear algebraic problems [10-15], with potential exponential speedup in runtime under the assumption of effective input from a quantum random access memory [16]. In machine learning, generative models represent another large class [9] which is widely used for both supervised and unsupervised learning [17, 18]. Here, we propose an efficient quantum algorithm for machine learning based on a quantum generative model. We prove that our proposed model is exponentially more powerful to represent probability distributions compared with classical generative models and has exponential speedup in training and inference at least for some instances under a reasonable assumption in computational complexity theory. Our result opens a new direction for quantum machine learning and offers a remarkable example in which a quantum algorithm shows exponential improvement over any classical algorithm in an important application field. Machine learning and artificial intelligence represent a very important application area which could be revolutionized by quantum computers with clever algorithms that offer exponential speedup [4, 5]. The candidate algorithms with potential exponential speedup so far rely on efficient quantum solution of linear system of equations or linear algebraic problems [12-15]. Those algorithms require quantum random access memory (QRAM) as a critical component in addition to a quantum computer. In a QRAM, the number of required quantum routers scales up exponentially with the number of qubits in those algorithms [16, 19]. This exponential overhead in resource requirement poses a significant challenge for its experimental implementation and is a caveat for fair comparison with corresponding classical algorithms [5, 20]. In this paper, we propose a quantum algorithm with potential exponential speedup for machine learning basedFigure 1: Classical and quantum generative models. A factor graph is a bipartite graph where one group of the vertices represent variables (denoted by circles) and the other group of vertices represent positive functions (denoted by squares) acting on connected variables. The corresponding probability distribution is given by the product of all these functions. Each variable connects to at most a constant number of functions which introduce correlations in the probability distribution.b,

Mechanistic models of single-neuron dynamics have been extensively studied in computational neuroscience. However, identifying which models can quantitatively reproduce empirically measured data has been challenging. We propose to overcome this limitation by using likelihood-free inference approaches (also known as Approximate Bayesian Computation, ABC) to perform full Bayesian inference on single-neuron models. Our approach builds on recent advances in ABC by learning a neural network which maps features of the observed data to the posterior distribution over parameters. We learn a Bayesian mixture-density network approximating the posterior over multiple rounds of adaptively chosen simulations. Furthermore, we propose an efficient approach for handling missing features and parameter settings for which the simulator fails, as well as a strategy for automatically learning relevant features using recurrent neural networks. On synthetic data, our approach efficiently estimates posterior distributions and recovers ground-truth parameters. On in-vitro recordings of membrane voltages, we recover multivariate posteriors over biophysical parameters, which yield model-predicted voltage traces that accurately match empirical data. Our approach will enable neuroscientists to perform Bayesian inference on complex neuron models without having to design model-specific algorithms, closing the gap between mechanistic and statistical approaches to single-neuron modelling.

Calcium imaging permits optical measurement of neural activity. Since intracellular calcium concentration is an indirect measurement of neural activity, computational tools are necessary to infer the true underlying spiking activity from fluorescence measurements. Bayesian model inversion can be used to solve this problem, but typically requires either computationally expensive MCMC sampling, or faster but approximate maximum-a-posteriori optimization. Here, we introduce a flexible algorithmic framework for fast, efficient and accurate extraction of neural spikes from imaging data. Using the framework of variational autoencoders, we propose to amortize inference by training a deep neural network to perform model inversion efficiently. The recognition network is trained to produce samples from the posterior distribution over spike trains. Once trained, performing inference amounts to a fast single forward pass through the network, without the need for iterative optimization or sampling. We show that amortization can be applied flexibly to a wide range of nonlinear generative models and significantly improves upon the state of the art in computation time, while achieving competitive accuracy. Our framework is also able to represent posterior distributions over spike-trains. We demonstrate the generality of our method by proposing the first probabilistic approach for separating backpropagating action potentials from putative synaptic inputs in calcium imaging of dendritic spines.

In this paper, we consider the block-sparse signals recovery problem in the context of multiple measurement vectors (MMV) with common row sparsity patterns. We develop a new method for recovery of common row sparsity MMV signals, where a pattern-coupled hierarchical Gaussian prior model is introduced to characterize both the block-sparsity of the coefficients and the statistical dependency between neighboring coefficients of the common row sparsity MMV signals. Unlike many other methods, the proposed method is able to automatically capture the block sparse structure of the unknown signal. Our method is developed using an expectation-maximization (EM) framework. Simulation results show that our proposed method offers competitive performance in recovering block-sparse common row sparsity pattern MMV signals.

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be represented as an undirected graph (or Markov random field), but most algorithms for learning this structure are restricted to the discrete or Gaussian cases. Our new approach allows for more realistic and accurate descriptions of the distribution in question, and in turn better estimates of its sparse Markov structure. Sparsity in the graph is of interest as it can accelerate inference, improve sampling methods, and reveal important dependencies between variables. The algorithm relies on exploiting the connection between the sparsity of the graph and the sparsity of transport maps, which deterministically couple one probability measure to another.

While all kinds of mixed data -from personal data, over panel and scientific data, to public and commercial data- are collected and stored, building probabilistic graphical models for these hybrid domains becomes more difficult. Users spend significant amounts of time in identifying the parametric form of the random variables (Gaussian, Poisson, Logit, etc.) involved and learning the mixed models. To make this difficult task easier, we propose the first trainable probabilistic deep architecture for hybrid domains that features tractable queries. It is based on Sum-Product Networks (SPNs) with piecewise polynomial leave distributions together with novel nonparametric decomposition and conditioning steps using the Hirschfeld-Gebelein-R\'enyi Maximum Correlation Coefficient. This relieves the user from deciding a-priori the parametric form of the random variables but is still expressive enough to effectively approximate any continuous distribution and permits efficient learning and inference. Our empirical evidence shows that the architecture, called Mixed SPNs, can indeed capture complex distributions across a wide range of hybrid domains.

Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal effects from observational data is the handling of confounders, factors that affect both an intervention and its outcome. A carefully designed observational study attempts to measure all important confounders. However, even if one does not have direct access to all confounders, there may exist noisy and uncertain measurement of proxies for confounders. We build on recent advances in latent variable modeling to simultaneously estimate the unknown latent space summarizing the confounders and the causal effect. Our method is based on Variational Autoencoders (VAE) which follow the causal structure of inference with proxies. We show our method is significantly more robust than existing methods, and matches the state-of-the-art on previous benchmarks focused on individual treatment effects.

Compression and computational efficiency in deep learning have become a problem of great significance. In this work, we argue that the most principled and effective way to attack this problem is by adopting a Bayesian point of view, where through sparsity inducing priors we prune large parts of the network. We introduce two novelties in this paper: 1) we use hierarchical priors to prune nodes instead of individual weights, and 2) we use the posterior uncertainties to determine the optimal fixed point precision to encode the weights. Both factors significantly contribute to achieving the state of the art in terms of compression rates, while still staying competitive with methods designed to optimize for speed or energy efficiency.