We propose Cooperative Training (CoT) for training generative models that measure a tractable density function for target data. CoT coordinately trains a generator $G$ and an auxiliary predictive mediator $M$. The training target of $M$ is to estimate a mixture density of the learned distribution $G$ and the target distribution $P$, and that of $G$ is to minimize the Jensen-Shannon divergence estimated through $M$. CoT achieves independent success without the necessity of pre-training via Maximum Likelihood Estimation or involving high-variance algorithms like REINFORCE. This low-variance algorithm is theoretically proved to be unbiased for both generative and predictive tasks. We also theoretically and empirically show the superiority of CoT over most previous algorithms, in terms of generative quality and diversity, predictive generalization ability and computational cost.

The purpose of this paper is to address the problem of learning dictionaries for multimodal datasets, i.e. datasets collected from multiple data sources. We present an algorithm called multimodal sparse Bayesian dictionary learning (MSBDL). The MSBDL algorithm is able to leverage information from all available data modalities through a joint sparsity constraint on each modality's sparse codes without restricting the coefficients themselves to be equal. Our framework offers a considerable amount of flexibility to practitioners and addresses many of the shortcomings of existing multimodal dictionary learning approaches. Unlike existing approaches, MSBDL allows the dictionaries for each data modality to have different cardinality. In addition, MSBDL can be used in numerous scenarios, from small datasets to extensive datasets with large dimensionality. MSBDL can also be used in supervised settings and allows for learning multimodal dictionaries concurrently with classifiers for each modality.

This paper investigates to what extent do cognitive biases affect human understanding of interpretable machine learning models, in particular of rules discovered from data. Twenty cognitive biases (illusions, effects) are covered, as are possibly effective debiasing techniques that can be adopted by designers of machine learning algorithms and software. While there seems no universal approach for eliminating all the identified cognitive biases, it follows from our analysis that the effect of most biases can be ameliorated by making rule-based models more concise. Due to lack of previous research, our review transfers general results obtained in cognitive psychology to the domain of machine learning. It needs to be succeeded by empirical studies specifically aimed at the machine learning domain.

In this Course you learn k-Nearest Neighbors & Naive Bayes Classification Methods. In pattern recognition, the k-nearest neighbors algorithm (k-NN) is a non-parametric method used for classification and regression. The k-NN algorithm is among the simplest of all machine learning algorithms. For classification, a useful technique can be to assign weight to the contributions of the neighbors, so that the nearer neighbors contribute more to the average than the more distant ones. The neighbors are taken from a set of objects for which the class (for k-NN classification).

The field of artificial neural networks has exploded during the 1980s due to its universal approximation capabilities, as can be seen in [1], but the lack of understanding of the underlying statistical and geometric features extracted from the analyzed signal discouraged significantly its usage among scientists and researchers, as can be seen in [2-3]. Since then, most of its usage has been relegated to applications where such understanding can be neglected, such as computer vision, nonlinear statespace estimators and other tasks related to control where exact algorithmic approaches are unknown or too difficult to implement, according to [3]. More recently, aiming to enlightening these black-boxes, several approaches have been under heavy development, such as variables contributions in the feed forward structure [4], visualization using saliency maps [5], generation of skeletal structures [6], fuzzy rule based evaluation of all permutations [3], extraction of functional relations using sensitivity analysis of input data [7], as many others. In a parallel way, other researchers have been successfully developing new kinds of feed-forward neural architectures that behave much more like a transparent box, where the extracted features can be directly evaluated and understood. Convolutional Neural Networks are a great example of such achievements, as can be seen in [8-10]. Despite its several layers, they can be employed on different types of tasks, including text classification, natural language processing, computer vision and so on, with a good understanding of what is happening behind the curtains. Manuscript received January 15, 2018. This work was supported in part by the FIPE (Institute of Economic Research Foundation) by means of a postdoctoral scholarship.

We consider a problem of multiclass classification, where the training sample $S_n = \{(X_i, Y_i)\}_{i=1}^n$ is generated from the model $\mathbb p(Y = m | X = x) = \theta_m(x)$, $1 \leq m \leq M$, and $\theta_1(x), \dots, \theta_M(x)$ are unknown Lipschitz functions. Given a test point $X$, our goal is to estimate $\theta_1(X), \dots, \theta_M(X)$. An approach based on nonparametric smoothing uses a localization technique, i.e. the weight of observation $(X_i, Y_i)$ depends on the distance between $X_i$ and $X$. However, local estimates strongly depend on localizing scheme. In our solution we fix several schemes $W_1, \dots, W_K$, compute corresponding local estimates $\widetilde\theta^{(1)}, \dots, \widetilde\theta^{(K)}$ for each of them and apply an aggregation procedure. We propose an algorithm, which constructs a convex combination of the estimates $\widetilde\theta^{(1)}, \dots, \widetilde\theta^{(K)}$ such that the aggregated estimate behaves approximately as well as the best one from the collection $\widetilde\theta^{(1)}, \dots, \widetilde\theta^{(K)}$. We also study theoretical properties of the procedure, prove oracle results and establish rates of convergence under mild assumptions.

We present and evaluate the Fast (conditional) Independence Test (FIT) -- a nonparametric conditional independence test. The test is based on the idea that when $P(X \mid Y, Z) = P(X \mid Y)$, $Z$ is not useful as a feature to predict $X$, as long as $Y$ is also a regressor. On the contrary, if $P(X \mid Y, Z) \neq P(X \mid Y)$, $Z$ might improve prediction results. FIT applies to thousand-dimensional random variables with a hundred thousand samples in a fraction of the time required by alternative methods. We provide an extensive evaluation that compares FIT to six extant nonparametric independence tests. The evaluation shows that FIT has low probability of making both Type I and Type II errors compared to other tests, especially as the number of available samples grows. Our implementation of FIT is publicly available.

It is well known that the problems of stochastic planning and probabilistic inference are closely related. This paper makes several contributions in this context for factored spaces where the complexity of solutions is challenging. First, we analyze the recently developed SOGBOFA heuristic, which performs stochastic planning by building an explicit computation graph capturing an approximate aggregate simulation of the dynamics. It is shown that the values computed by this algorithm are identical to the approximation provided by Belief Propagation (BP). Second, as a consequence of this observation, we show how ideas on lifted BP can be used to develop a lifted version of SOGBOFA. Unlike implementations of lifted BP, Lifted SOGBOFA has a very simple implementation as a dynamic programming version of the original graph construction. Third, we show that the idea of graph construction for aggregate simulation can be used to solve marginal MAP (MMAP) problems in Bayesian networks, where MAP variables are constrained to be at roots of the network. This yields a novel algorithm for MMAP for this subclass. An experimental evaluation illustrates the advantage of Lifted SOGBOFA for planning.

We introduce a generalized dual decomposition bound for computing the maximum expected utility of influence diagrams based on the dual decomposition method generalized to $L^p$ space.  The main goal is to devise an approximation scheme free from translations required by existing variational approaches while exploiting the local structure of sum of utility functions as well as the conditional independence of probability functions.  In this work, the generalized dual decomposition method is applied to the algebraic framework called valuation algebra for influence diagrams which handles probability and expected utility as a pair. The proposed approach allows a sequential decision problem to be decomposed as a collection of sub-decision problems of bounded complexity and the upper bound of maximum expected utility to be computed by combining the local expected utilities. Thus, it has a flexible control of space and time complexity for computing the bound.  In addition, the upper bounds can be further minimized by reparameterizing the utility functions. Since the global objective function for the minimization is nonconvex, we present a gradient-based local search algorithm in which the outer loop controls the randomization of the initial configurations and the inner loop tightens the upper-bound based on block coordinate descent with gradients perturbed by a random noise. The experimental evaluation demonstrates highlights of the proposed approach on finite horizon MDP/POMDP instances.

Treatable infectious diseases are a critical challenge for public health. Outreach campaigns can encourage undiagnosed patients to seek treatment but must be carefully targeted to make the most efficient use of limited resources. We present an algorithm to optimally allocate limited outreach resources among demographic groups in the population. The algorithm uses a novel multiagent model of disease spread which both captures the underlying population dynamics and is amenable to optimization. Our algorithm extends, with provable guarantees, to a stochastic setting where we have only a distribution over parameters such as the contact pattern between agents. We evaluate our algorithm on two instances where this distribution is inferred from real world data: tuberculosis in India and gonorrhea in the United States. Our algorithm produces a policy which is predicted to avert an average of least 8,000 person-years of tuberculosis and 20,000 person-years of gonorrhea annually compared to current policy.