Motivated by a real-world problem, we study a novel budgeted optimization problem where the goal is to optimize an unknown function f(.) given a budget by requesting a sequence of samples from the function. In our setting, however, evaluating the function at precisely specified points is not practically possible due to prohibitive costs. Instead, we can only request constrained experiments. A constrained experiment, denoted by Q, specifies a subset of the input space for the experimenter to sample the function from. The outcome of Q includes a sampled experiment x, and its function output f(x). Importantly, as the constraints of Q become looser, the cost of fulfilling the request decreases, but the uncertainty about the location x increases. Our goal is to manage this trade-off by selecting a set of constrained experiments that best optimize f(.) within the budget. We study this problem in two different settings, the non-sequential (or batch) setting where a set of constrained experiments is selected at once, and the sequential setting where experiments are selected one at a time. We evaluate our proposed methods for both settings using synthetic and real functions. The experimental results demonstrate the efficacy of the proposed methods.

This paper proposes CF-NADE, a neural autoregressive architecture for collaborative filtering (CF) tasks, which is inspired by the Restricted Boltzmann Machine (RBM) based CF model and the Neural Autoregressive Distribution Estimator (NADE). We first describe the basic CF-NADE model for CF tasks. Then we propose to improve the model by sharing parameters between different ratings. A factored version of CF-NADE is also proposed for better scalability. Furthermore, we take the ordinal nature of the preferences into consideration and propose an ordinal cost to optimize CF-NADE, which shows superior performance. Finally, CF-NADE can be extended to a deep model, with only moderately increased computational complexity. Experimental results show that CF-NADE with a single hidden layer beats all previous state-of-the-art methods on MovieLens 1M, MovieLens 10M, and Netflix datasets, and adding more hidden layers can further improve the performance.

We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive) latent variable models such as hidden Markov models, POMDPs are more challenging since the learner interacts with the environment and possibly changes the future observations in the process. We devise a learning algorithm running through episodes, in each episode we employ spectral techniques to learn the POMDP parameters from a trajectory generated by a fixed policy. At the end of the episode, an optimization oracle returns the optimal memoryless planning policy which maximizes the expected reward based on the estimated POMDP model. We prove an order-optimal regret bound with respect to the optimal memoryless policy and efficient scaling with respect to the dimensionality of observation and action spaces.

Variational inference (VI) combined with data subsampling enables approximate posterior inference over large data sets, but suffers from poor local optima. We first formulate a deterministic annealing approach for the generic class of conditionally conjugate exponential family models. This approach uses a decreasing temperature parameter which deterministically deforms the objective during the course of the optimization. A well-known drawback to this annealing approach is the choice of the cooling schedule. We therefore introduce variational tempering, a variational algorithm that introduces a temperature latent variable to the model. In contrast to related work in the Markov chain Monte Carlo literature, this algorithm results in adaptive annealing schedules. Lastly, we develop local variational tempering, which assigns a latent temperature to each data point; this allows for dynamic annealing that varies across data. Compared to the traditional VI, all proposed approaches find improved predictive likelihoods on held-out data.

Creating mood sensing technology has become very popular in recent years. There is a wide range of companies trying to detect your emotions from what you write, the tone of your voice, or from the expressions on your face. All of these companies offer their technology online through cloud-based programming interfaces (APIs). As part of my offline emotion sensing hardware (Project Jammin), I have already built early prototypes of facial expression and speech content recognition for emotion detection. In this short article I describe the missing part, a voice tone analyzer.

If you are a software developer who wants to learn how machine learning models work and how to apply them effectively, this book is for you. Familiarity with machine learning fundamentals and Python will be helpful, but is not essential. This book examines machine learning models including logistic regression, decision trees, and support vector machines, and applies them to common problems such as categorizing documents and classifying images. It begins with the fundamentals of machine learning, introducing you to the supervised-unsupervised spectrum, the uses of training and test data, and evaluating models. You will learn how to use generalized linear models in regression problems, as well as solve problems with text and categorical features. You will be acquainted with the use of logistic regression, regularization, and the various loss functions that are used by generalized linear models.

This paper proposes a new sampling scheme based on Langevin dynamics that is applicable within pseudo-marginal and particle Markov chain Monte Carlo algorithms. We investigate this algorithm's theoretical properties under standard asymptotics, which correspond to an increasing dimension of the parameters, $n$. Our results show that the behaviour of the algorithm depends crucially on how accurately one can estimate the gradient of the log target density. If the error in the estimate of the gradient is not sufficiently controlled as dimension increases, then asymptotically there will be no advantage over the simpler random-walk algorithm. However, if the error is sufficiently well-behaved, then the optimal scaling of this algorithm will be $O(n^{-1/6})$ compared to $O(n^{-1/2})$ for the random walk. Our theory also gives guidelines on how to tune the number of Monte Carlo samples in the likelihood estimate and the proposal step-size.

Hidden Markov Models (HMM) have been used for several years in many time series analysis or pattern recognitions tasks. HMM are often trained by means of the Baum-Welch algorithm which can be seen as a special variant of an expectation maximization (EM) algorithm. Second-order training techniques such as Variational Bayesian Inference (VI) for probabilistic models regard the parameters of the probabilistic models as random variables and define distributions over these distribution parameters, hence the name of this technique. VI can also bee regarded as a special case of an EM algorithm. In this article, we bring both together and train HMM with multivariate Gaussian output distributions with VI. The article defines the new training technique for HMM. An evaluation based on some case studies and a comparison to related approaches is part of our ongoing work.

We learn the structure of a Markov Network between two groups of random variables from joint observations. Since modelling and learning the full MN structure may be hard, learning the links between two groups directly may be a preferable option. We introduce a novel concept called the \emph{partitioned ratio} whose factorization directly associates with the Markovian properties of random variables across two groups. A simple one-shot convex optimization procedure is proposed for learning the \emph{sparse} factorizations of the partitioned ratio and it is theoretically guaranteed to recover the correct inter-group structure under mild conditions. The performance of the proposed method is experimentally compared with the state of the art MN structure learning methods using ROC curves. Real applications on analyzing bipartisanship in US congress and pairwise DNA/time-series alignments are also reported.

Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliary inverse temperature variable. Our method exploits the multinomial probability law of the inverse temperatures, and provides estimates of the partition function in terms of a simple quotient of Rao-Blackwellized marginal inverse temperature probability estimates, which are updated while sampling. We show that the method has interesting connections with several alternative popular methods, and offers some significant advantages. In particular, we empirically find that the new method provides more accurate estimates than Annealed Importance Sampling when calculating partition functions of large Restricted Boltzmann Machines (RBM); moreover, the method is sufficiently accurate to track training and validation log-likelihoods during learning of RBMs, at minimal computational cost.