Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding parameters with the maximum likelihood is NP-hard even in very simple settings. In recent years, provably efficient algorithms were nevertheless developed for models with linear structures: topic models, mixture models, hidden markov models, etc. These algorithms use matrix or tensor decomposition, and make some reasonable assumptions about the parameters of the underlying model. But matrix or tensor decomposition seems of little use when the latent variable model has nonlinearities. The current paper shows how to make progress: tensor decomposition is applied for learning the single-layer {\em noisy or} network, which is a textbook example of a Bayes net, and used for example in the classic QMR-DT software for diagnosing which disease(s) a patient may have by observing the symptoms he/she exhibits. The technical novelty here, which should be useful in other settings in future, is analysis of tensor decomposition in presence of systematic error (i.e., where the noise/error is correlated with the signal, and doesn't decrease as number of samples goes to infinity). This requires rethinking all steps of tensor decomposition methods from the ground up. For simplicity our analysis is stated assuming that the network parameters were chosen from a probability distribution but the method seems more generally applicable.

Big data trend has enforced the data-centric systems to have continuous fast data streams. In recent years, real-time analytics on stream data has formed into a new research field, which aims to answer queries about what-is-happening-now with a negligible delay. The real challenge with real-time stream data processing is that it is impossible to store instances of data, and therefore online analytical algorithms are utilized. To perform real-time analytics, pre-processing of data should be performed in a way that only a short summary of stream is stored in main memory. In addition, due to high speed of arrival, average processing time for each instance of data should be in such a way that incoming instances are not lost without being captured. Lastly, the learner needs to provide high analytical accuracy measures. Sentinel is a distributed system written in Java that aims to solve this challenge by enforcing both the processing and learning process to be done in distributed form. Sentinel is built on top of Apache Storm, a distributed computing platform. Sentinels learner, Vertical Hoeffding Tree, is a parallel decision tree-learning algorithm based on the VFDT, with ability of enabling parallel classification in distributed environments. Sentinel also uses SpaceSaving to keep a summary of the data stream and stores its summary in a synopsis data structure. Application of Sentinel on Twitter Public Stream API is shown and the results are discussed.

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: 1) where the marginal distributions are Poisson, 2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent discussion section.

Most tasks in Machine Learning can be reduced to classification tasks. For example, we have a medical dataset and we want to classify who has diabetes (positive class) and who doesn't (negative class). We have a dataset from the financial world and want to know which customers will default on their credit (positive class) and which customers will not (negative class). To do this, we can train a Classifier with a'training dataset' and after such a Classifier is trained (we have determined its model parameters) and can accurately classify the training set, we can use it to classify new data (test set). If the training is done properly, the Classifier should predict the class probabilities of the new data with a similar accuracy.

Editor's note: The following is an interview with Columbia University Professor Andrew Gelman conducted by Marketing scientist Kevin Gray, in which Gelman spells out the ABCs of Bayesian statistics. Andrew Gelman: Bayesian statistics uses the mathematical rules of probability to combines data with "prior information" to give inferences which (if the model being used is correct) are more precise than would be obtained by either source of information alone. Classical statistical methods avoid prior distributions. In classical statistics, you might include in your model a predictor (for example), or you might exclude it, or you might pool it as part of some larger set of predictors in order to get a more stable estimate. These are pretty much your only choices.

Differential privacy formalises privacy-preserving mechanisms that provide access to a database. We pose the question of whether Bayesian inference itself can be used directly to provide private access to data, with no modification. The answer is affirmative: under certain conditions on the prior, sampling from the posterior distribution can be used to achieve a desired level of privacy and utility. To do so, we generalise differential privacy to arbitrary dataset metrics, outcome spaces and distribution families. This allows us to also deal with non-i.i.d or non-tabular datasets. We prove bounds on the sensitivity of the posterior to the data, which gives a measure of robustness. We also show how to use posterior sampling to provide differentially private responses to queries, within a decision-theoretic framework. Finally, we provide bounds on the utility and on the distinguishability of datasets. The latter are complemented by a novel use of Le Cam's method to obtain lower bounds. All our general results hold for arbitrary database metrics, including those for the common definition of differential privacy. For specific choices of the metric, we give a number of examples satisfying our assumptions.

The vast majority of current machine learning algorithms are designed to predict single responses or a vector of responses, yet many types of response are more naturally organized as matrices or higher-order tensor objects where characteristics are shared across modes. We present a new machine learning algorithm BaTFLED (Bayesian Tensor Factorization Linked to External Data) that predicts values in a three-dimensional response tensor using input features for each of the dimensions. BaTFLED uses a probabilistic Bayesian framework to learn projection matrices mapping input features for each mode into latent representations that multiply to form the response tensor. By utilizing a Tucker decomposition, the model can capture weights for interactions between latent factors for each mode in a small core tensor. Priors that encourage sparsity in the projection matrices and core tensor allow for feature selection and model regularization. This method is shown to far outperform elastic net and neural net models on 'cold start' tasks from data simulated in a three-mode structure. Additionally, we apply the model to predict dose-response curves in a panel of breast cancer cell lines treated with drug compounds that was used as a Dialogue for Reverse Engineering Assessments and Methods (DREAM) challenge.

We evaluate the uncertainty quality in neural networks using anomaly detection. We extract uncertainty measures (e.g. entropy) from the predictions of candidate models, use those measures as features for an anomaly detector, and gauge how well the detector differentiates known from unknown classes. We assign higher uncertainty quality to candidate models that lead to better detectors. We also propose a novel method for sampling a variational approximation of a Bayesian neural network, called One-Sample Bayesian Approximation (OSBA). We experiment on two datasets, MNIST and CIFAR10. We compare the following candidate neural network models: Maximum Likelihood, Bayesian Dropout, OSBA, and --- for MNIST --- the standard variational approximation. We show that Bayesian Dropout and OSBA provide better uncertainty information than Maximum Likelihood, and are essentially equivalent to the standard variational approximation, but much faster.

The computational properties of neural systems are often thought to be implemented in terms of their network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit (MSU) recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a state space representation of the dynamics, but would wish to have access to its governing equations for in-depth analysis. Recurrent neural networks (RNNs) are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective. Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs (PLRNNs) within the statistical framework of state space models, which accounts for noise in both the underlying latent dynamics and the observation process. The Expectation-Maximization algorithm is used to infer the latent state distribution, through a global Laplace approximation, and the PLRNN parameters iteratively. After validating the procedure on toy examples, the approach is applied to MSU recordings from the rodent anterior cingulate cortex obtained during performance of a classical working memory task, delayed alternation. A model with 5 states turned out to be sufficient to capture the essential computational dynamics underlying task performance, including stimulus-selective delay activity. The estimated models were rarely multi-stable, but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point. In summary, the present work advances a semi-analytical (thus reasonably fast) maximum-likelihood estimation framework for PLRNNs that may enable to recover the relevant dynamics underlying observed neuronal time series, and directly link them to computational properties.

In our previous post, we showed the examples of using linear models and machine learning approach for forecasting sales time series. Sometimes we need to forecast not only more probable values of sales but also their distribution. Especially we need it in the risk analysis for assessing different risks related to sales dynamics. In this case we need to take into account sales distributions and dependencies between sales time series features (e.g. One can consider sales as a stochastic variable with some marginal distributions.