We construct $\bf genRBF$ kernel, which generalizes the classical Gaussian RBF kernel to the case of incomplete data. We model the uncertainty contained in missing attributes making use of data distribution and associate every point with a conditional probability density function. This allows to embed incomplete data into the function space and to define a kernel between two missing data points based on scalar product in $L_2$. Experiments show that introduced kernel applied to SVM classifier gives better results than other state-of-the-art methods, especially in the case when large number of features is missing. Moreover, it is easy to implement and can be used together with any kernel approaches with no additional modifications.

In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an algorithm for identifying such linearly separable class utilizing linear programming. We described three application cases including an assumption of linear separability, Gaussian distribution, and the case of linear separability in transformed space of kernel functions. Finally, we demonstrated the work of the proposed algorithm on the USPS dataset and analyzed the relationship of the performance of the algorithm and the size of the initially labeled sample.

In the present paper, we studied a Dynamic Stochastic Block Model (DSBM) under the assumptions that the connection probabilities, as functions of time, are smooth and that at most $s$ nodes can switch their class memberships between two consecutive time points. We estimate the edge probability tensor by a kernel-type procedure and extract the group memberships of the nodes by spectral clustering. The procedure is computationally viable, adaptive to the unknown smoothness of the functional connection probabilities, to the rate $s$ of membership switching and to the unknown number of clusters. In addition, it is accompanied by non-asymptotic guarantees for the precision of estimation and clustering.

Nesterov's momentum trick is famously known for accelerating gradient descent, and has been proven useful in building fast iterative algorithms. However, in the stochastic setting, counterexamples exist and prevent Nesterov's momentum from providing similar acceleration, even if the underlying problem is convex. We introduce $\mathtt{Katyusha}$, a direct, primal-only stochastic gradient method to fix this issue. It has a provably accelerated convergence rate in convex (off-line) stochastic optimization. The main ingredient is $\textit{Katyusha momentum}$, a novel "negative momentum" on top of Nesterov's momentum. It can be incorporated into a variance-reduction based algorithm and speed it up, both in terms of $\textit{sequential and parallel}$ performance. Since variance reduction has been successfully applied to a growing list of practical problems, our paper suggests that in each of such cases, one could potentially try to give Katyusha a hug.

I would probably spend the time on simple (yet useful) algorithms that are representative of these fields (and maybe save reinforcement learning for later).

Introduce yourself to the basics of data science and leave armed with practical experience extracting value from big data. This course teaches the basic techniques of data science, including both SQL and NoSQL solutions for massive data management (e.g., MapReduce and contemporaries), algorithms for data mining (e.g., clustering and association rule mining), and basic statistical modelling (e.g., linear and non-linear regression).

Machine Learning is getting a lot more air time these days but are we actually sure what it is? It gives computers the ability to learn without being explicitly programmed" (Arthur Samuel, 1959). This is an old quote but it has held the test of time. But,how can computers "learn" – have we really reached the age of artificial intelligence where they will take over the world and make humans redundant? Let's explore the core of the definition: the ability to learn What this really means is there are a set of algorithms that, rather than simply following a static set of program instructions, they can make data driven predictions, or decisions through building a model. Supervised learning – The computer is presented with example inputs (training data) and their desired outputs, given by a "teacher", and the goal is to learn a general rule that maps inputs to outputs. The "easiest" example of supervised learning is a decision tree – this uses a tree-like graph or model of decisions and ...

When I first started out learning about machine learning algorithms, it turned out to be quite a task to gain an intuition of what the algorithms are doing. Not just because it was difficult to understand all the mathematical theory and notations, but it was also plain boring. When I turned to online tutorials for answers, I could again only see equations or high level explanations without going through the detail in a majority of the cases. It was then that one of my data science colleagues introduced me to the concept of working out an algorithm in an excel sheet. And that worked wonders for me.

By using Python to glean value from your raw data, you can simplify the often complex journey from data to value. In this practical, hands-on course, learn how to use Python for data preparation, data munging, data visualization, and predictive analytics. She helps to provide you with a working understanding of machine learning, as well as outlier analysis, cluster analysis, and network analysis. Plus, Lillian explains how to create web-based data visualizations with Plot.ly, and how to use Python to scrape the web and capture your own data sets.

We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper we propose novel algorithms to optimize the forward and reverse forms of the KL divergence, as well as the alpha-divergence which contains these two as limiting cases. Unlike previous approaches, our algorithms do not make approximations to the divergences being optimized, but use Monte Carlo integration techniques to derive unbiased algorithms for direct optimization. We assess performance on radar and sensor tracking, and options pricing problems, showing general improvement over the UKF and EKF, as well as competitive performance with particle filtering.