There are multiple ways to classify data with machine learning. You could run a logistic regression, use decision trees, or build a neural network to accomplish the task. In 1963, Vladimir Vapnik and Alexey Chervonenkis developed another classification tool, the support vector machine. Vapnik refined this classification method in the 1990's and extended uses for SVMs. Support vector machines have become a great tool for the data scientist.

We study the conditions under which one is able to efficiently apply variance-reduction and acceleration schemes on finite sum optimization problems. First, we show that, perhaps surprisingly, the finite sum structure by itself, is not sufficient for obtaining a complexity bound of $\tilde{\cO}((n+L/\mu)\ln(1/\epsilon))$ for $L$-smooth and $\mu$-strongly convex individual functions - one must also know which individual function is being referred to by the oracle at each iteration. Next, we show that for a broad class of first-order and coordinate-descent finite sum algorithms (including, e.g., SDCA, SVRG, SAG), it is not possible to get an `accelerated' complexity bound of $\tilde{\cO}((n+\sqrt{n L/\mu})\ln(1/\epsilon))$, unless the strong convexity parameter is given explicitly. Lastly, we show that when this class of algorithms is used for minimizing $L$-smooth and convex finite sums, the optimal complexity bound is $\tilde{\cO}(n+L/\epsilon)$, assuming that (on average) the same update rule is used in every iteration, and $\tilde{\cO}(n+\sqrt{nL/\epsilon})$, otherwise.

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems, which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastics SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy, and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential, and the projected dynamics of a two-dimensional diffusion process. 1 I. INTRODUCTION The last decade has seen a dramatic increase in our ability to collect or produce large amounts of high resolution and high dimensional data associated with complex physical and chemical systems, both by means of experimental measurements or computer simulations. In many different scientific fields, ranging from high energy physics to neuroscience, the "bigdata" problem has spurred interest in data analysis methods that can condense massive datasets into a minimal amount of essential information and/or can detect relevant patterns and anomalies in the distribution of the data.

In this paper, we propose a new algorithm for learning general latent-variable probabilistic graphical models using the techniques of predictive state representation, instrumental variable regression, and reproducing-kernel Hilbert space embeddings of distributions. Under this new learning framework, we first convert latent-variable graphical models into corresponding latent-variable junction trees, and then reduce the hard parameter learning problem into a pipeline of supervised learning problems, whose results will then be used to perform predictive belief propagation over the latent junction tree during the actual inference procedure. We then give proofs of our algorithm's correctness, and demonstrate its good performance in experiments on one synthetic dataset and two real-world tasks from computational biology and computer vision -- classifying DNA splice junctions and recognizing human actions in videos.

Kernel methods are popular in clustering due to their generality and discriminating power. However, we show that many kernel clustering criteria have density biases theoretically explaining some practically significant artifacts empirically observed in the past. For example, we provide conditions and formally prove the density mode isolation bias in kernel K-means for a common class of kernels. We call it Breiman's bias due to its similarity to the histogram mode isolation previously discovered by Breiman in decision tree learning with Gini impurity. We also extend our analysis to other popular kernel clustering methods, e.g. average/normalized cut or dominant sets, where density biases can take different forms. For example, splitting isolated points by cut-based criteria is essentially the sparsest subset bias, which is the opposite of the density mode bias. Our findings suggest that a principled solution for density biases in kernel clustering should directly address data inhomogeneity. We show that density equalization can be implicitly achieved using either locally adaptive weights or locally adaptive kernels. Moreover, density equalization makes many popular kernel clustering objectives equivalent. Our synthetic and real data experiments illustrate density biases and proposed solutions. We anticipate that theoretical understanding of kernel clustering limitations and their principled solutions will be important for a broad spectrum of data analysis applications across the disciplines.

The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued signal into its quadrature component. In this paper, we define a probabilistic generalization of this approach. We model the observable real-valued signal as the real part of a latent complex-valued Gaussian process. In order to obtain the appropriate statistical relationship between its real and imaginary parts, we define two new classes of complex-valued covariance functions. Through an analysis of simulated chirplets and stochastic oscillations, we show that the resulting Gaussian process complex-valued signal provides a better estimate of the instantaneous amplitude and frequency than the established approaches. Furthermore, the complex-valued Gaussian process regression allows to incorporate prior information about the structure in signal and noise and thereby to tailor the analysis to the features of the signal. As a example, we analyze the non-stationary dynamics of brain oscillations in the alpha band, as measured using magneto-encephalography.

Many problems in artificial intelligence require adaptively making a sequence of decisions with uncertain outcomes under partial observability. Solving such stochastic optimization problems is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. In addition to providing performance guarantees for both stochastic maximization and coverage, adaptive submodularity can be exploited to drastically speed up the greedy algorithm by using lazy evaluations. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse AI applications including management of sensing resources, viral marketing and active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases, improve approximation guarantees and handle natural generalizations.

Here you can find links to the various Quick Start Guides to get a brief walkthrough of the basics of the using the Nexosis API. By following these walkthroughs using sample datasets, you will learn all of the steps needed to make predictions and forecasts using the Nexosis API. This is a Quick Start Guide that introduces the basics of using the Nexosis API to build a Regression model and then how to use that model to make a series of predictions. This Quick Start introduces how to use the Nexosis API to build Time Series based linear-regression model. By following this walkthrough, which uses a sample dataset, you will learn all of the steps needed to make forecasts using the Nexosis API.

My book'Practical Machine Learning with R and Python – Machine Learning in stereo' is now available in both paperback ($9.99) and kindle ($6.97/Rs449) versions. In this book I implement some of the most common, but important Machine Learning algorithms in R and equivalent Python code. This is almost like listening to parallel channels of music in stereo! This book is ideal both for beginners and the experts in R and/or Python. Those starting their journey into datascience and ML will find the first 3 chapters useful, as they touch upon the most important programming constructs in R and Python and also deal with equivalent statements in R and Python.

Count-based exploration algorithms are known to perform near-optimally when used in conjunction with tabular reinforcement learning (RL) methods for solving small discrete Markov decision processes (MDPs). It is generally thought that count-based methods cannot be applied in high-dimensional state spaces, since most states will only occur once. Recent deep RL exploration strategies are able to deal with high-dimensional continuous state spaces through complex heuristics, often relying on optimism in the face of uncertainty or intrinsic motivation. In this work, we describe a surprising finding: a simple generalization of the classic count-based approach can reach near state-of-the-art performance on various high-dimensional and/or continuous deep RL benchmarks. States are mapped to hash codes, which allows to count their occurrences with a hash table. These counts are then used to compute a reward bonus according to the classic count-based exploration theory. We find that simple hash functions can achieve surprisingly good results on many challenging tasks. Furthermore, we show that a domain-dependent learned hash code may further improve these results. Detailed analysis reveals important aspects of a good hash function: 1) having appropriate granularity and 2) encoding information relevant to solving the MDP. This exploration strategy achieves near state-of-the-art performance on both continuous control tasks and Atari 2600 games, hence providing a simple yet powerful baseline for solving MDPs that require considerable exploration.