In this week's Whiteboard Walkthrough Ted Dunning, Chief Application Architect at MapR, explains in detail how to use streaming IoT sensor data from handsets and devices as well as cell tower data to detect strange anomalies. He takes us from best practices for data architecture, including the advantages of multi-master writes with MapR Streams, through analysis of the telecom data using clustering methods to discover normal and anomalous behaviors. I'd like to talk a little bit about data processing in the context of telecom. In particular, what I'll be talking about is how to extend some of the ideas that we've talked about in other videos about anomaly detection to the particular case of telecom data. This is very different than some of the other data that we've been talking about.

In "Components of Time Series Data", I discussed the components of time series data. In time series analysis, we assume that the data consist of a systematic pattern (usually a set of identifiable components) and random noise (error), which often makes the pattern difficult to identify. Most time series analysis techniques involve some form of filtering out noise to make the pattern more noticeable. Though I have discussed other components of time series data, we can describe most time series patterns in terms of two basic classes of components: trend and seasonality. The former represents a general systematic linear or nonlinear component that changes over time and does not repeat, or at least does not repeat within the time range captured by our data (e.g., a plateau followed by a period of exponential growth).

Independent component analysis (ICA) is the most popular method for blind source separation (BSS) with a diverse set of applications, such as biomedical signal processing, video and image analysis, and communications. Maximum likelihood (ML), an optimal theoretical framework for ICA, requires knowledge of the true underlying probability density function (PDF) of the latent sources, which, in many applications, is unknown. ICA algorithms cast in the ML framework often deviate from its theoretical optimality properties due to poor estimation of the source PDF. Therefore, accurate estimation of source PDFs is critical in order to avoid model mismatch and poor ICA performance. In this paper, we propose a new and efficient ICA algorithm based on entropy maximization with kernels, (ICA-EMK), which uses both global and local measuring functions as constraints to dynamically estimate the PDF of the sources with reasonable complexity. In addition, the new algorithm performs optimization with respect to each of the cost function gradient directions separately, enabling parallel implementations on multi-core computers. We demonstrate the superior performance of ICA-EMK over competing ICA algorithms using simulated as well as real-world data.

In this paper we study the problem of recovering a structured but unknown parameter ${\bf{\theta}}^*$ from $n$ nonlinear observations of the form $y_i=f(\langle {\bf{x}}_i,{\bf{\theta}}^*\rangle)$ for $i=1,2,\ldots,n$. We develop a framework for characterizing time-data tradeoffs for a variety of parameter estimation algorithms when the nonlinear function $f$ is unknown. This framework includes many popular heuristics such as projected/proximal gradient descent and stochastic schemes. For example, we show that a projected gradient descent scheme converges at a linear rate to a reliable solution with a near minimal number of samples. We provide a sharp characterization of the convergence rate of such algorithms as a function of sample size, amount of a-prior knowledge available about the parameter and a measure of the nonlinearity of the function $f$. These results provide a precise understanding of the various tradeoffs involved between statistical and computational resources as well as a-prior side information available for such nonlinear parameter estimation problems.

Applied machine learning is a tapestry of breakthroughs and mindset shifts. Understanding the role of randomness in machine learning algorithms is one of those breakthroughs. Once you get it, you will see things differently. You will also start to see the abuses everywhere. In this post, I want to gently open your eyes to the role of random numbers in machine learning.

In this paper, we propose a general framework to learn a robust large-margin binary classifier when corrupt measurements, called anomalies, caused by sensor failure might be present in the training set. The goal is to minimize the generalization error of the classifier on non-corrupted measurements while controlling the false alarm rate associated with anomalous samples. By incorporating a non-parametric regularizer based on an empirical entropy estimator, we propose a Geometric-Entropy-Minimization regularized Maximum Entropy Discrimination (GEM-MED) method to learn to classify and detect anomalies in a joint manner. We demonstrate using simulated data and a real multimodal data set. Our GEM-MED method can yield improved performance over previous robust classification methods in terms of both classification accuracy and anomaly detection rate.

This paper deals with a natural stochastic optimization procedure derived from the so-called Heavy-ball method differential equation, which was introduced by Polyak in the 1960s with his seminal contribution [Pol64]. The Heavy-ball method is a second-order dynamics that was investigated to minimize convex functions f . The family of second-order methods recently received a large amount of attention, until the famous contribution of Nesterov [Nes83], leading to the explosion of large-scale optimization problems. This work provides an in-depth description of the stochastic heavy-ball method, which is an adaptation of the deterministic one when only unbiased evalutions of the gradient are available and used throughout the iterations of the algorithm. We first describe some almost sure convergence results in the case of general non-convex coercive functions f . We then examine the situation of convex and strongly convex potentials and derive some non-asymptotic results about the stochastic heavy-ball method. We end our study with limit theorems on several rescaled algorithms.

We present a sparse estimation and dictionary learning framework for compressed fiber sensing based on a probabilistic hierarchical sparse model. To handle severe dictionary coherence, selective shrinkage is achieved using a Weibull prior, which can be related to non-convex optimization with $p$-norm constraints for $0 < p < 1$. In addition, we leverage the specific dictionary structure to promote collective shrinkage based on a local similarity model. This is incorporated in form of a kernel function in the joint prior density of the sparse coefficients, thereby establishing a Markov random field-relation. Approximate inference is accomplished using a hybrid technique that combines Hamilton Monte Carlo and Gibbs sampling. To estimate the dictionary parameter, we pursue two strategies, relying on either a deterministic or a probabilistic model for the dictionary parameter. In the first strategy, the parameter is estimated based on alternating estimation. In the second strategy, it is jointly estimated along with the sparse coefficients. The performance is evaluated in comparison to an existing method in various scenarios using simulations and experimental data.

Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of the SGLD with a 1st-order Euler integrator have recently been studied, corresponding theory for general SG-MCMCs has not been explored. In this paper we consider general SG-MCMCs with high-order integrators, and develop theory to analyze finite-time convergence properties and their asymptotic invariant measures. Our theoretical results show faster convergence rates and more accurate invariant measures for SG-MCMCs with higher-order integrators. For example, with the proposed efficient 2nd-order symmetric splitting integrator, the {\em mean square error} (MSE) of the posterior average for the SGHMC achieves an optimal convergence rate of $L^{-4/5}$ at $L$ iterations, compared to $L^{-2/3}$ for the SGHMC and SGLD with 1st-order Euler integrators. Furthermore, convergence results of decreasing-step-size SG-MCMCs are also developed, with the same convergence rates as their fixed-step-size counterparts for a specific decreasing sequence. Experiments on both synthetic and real datasets verify our theory, and show advantages of the proposed method in two large-scale real applications.

The hybrid clustering-classification neural network is proposed. This network allows increasing a quality of information processing under the condition of overlapping classes due to the rational choice of a learning rate parameter and introducing a special procedure of fuzzy reasoning in the clustering process, which occurs both with an external learning signal (supervised) and without the one (unsupervised). As similarity measure neighborhood function or membership one, cosine structures are used, which allow to provide a high flexibility due to self-learning-learning process and to provide some new useful properties. Many realized experiments have confirmed the efficiency of proposed hybrid clustering-classification neural network; also, this network was used for solving diagnostics task of reactive arthritis.