Multi-output learning aims to simultaneously predict multiple outputs given an input. It is an important learning problem due to the pressing need for sophisticated decision making in real-world applications. Inspired by big data, the 4Vs characteristics of multi-output imposes a set of challenges to multi-output learning, in terms of the volume, velocity, variety and veracity of the outputs. Increasing number of works in the literature have been devoted to the study of multi-output learning and the development of novel approaches for addressing the challenges encountered. However, it lacks a comprehensive overview on different types of challenges of multi-output learning brought by the characteristics of the multiple outputs and the techniques proposed to overcome the challenges. This paper thus attempts to fill in this gap to provide a comprehensive review on this area. We first introduce different stages of the life cycle of the output labels. Then we present the paradigm on multi-output learning, including its myriads of output structures, definitions of its different sub-problems, model evaluation metrics and popular data repositories used in the study. Subsequently, we review a number of state-of-the-art multi-output learning methods, which are categorized based on the challenges.

We consider K-means clustering in networked environments (e.g., internet of things (IoT) and sensor networks) where data is inherently distributed across nodes and processing power at each node may be limited. We consider a clustering algorithm referred to as networked K-means, or N K-means, which relies only on local neighborhood information exchange. Information exchange is limited to low-dimensional statistics and not raw data at the agents. The proposed approach develops a parametric family of multi-agent clustering objectives (parameterized by ρ) and associated distributed N K-means algorithms (also parameterized by ρ). The NK-means algorithm with parameter ρ converges to a set of fixed points relative to the associated multi-agent objective (designated as generalized minima). By appropriate choice of ρ, the set of generalized minima may be brought arbitrarily close to the set of Lloyd's minima. Thus, the NK-means algorithm may be used to compute Lloyd's minima of the collective dataset up to arbitrary accuracy. Keywords: K-means clustering, Lloyd's minima, distributed algorithms, distributed machine learning, network information processing

A weighted random survival forest is presented in the paper. It can be regarded as a modification of the random forest improving its performance. The main idea underlying the proposed model is to replace the standard procedure of averaging used for estimation of the random survival forest hazard function by weighted avaraging where the weights are assigned to every tree and can be veiwed as training paremeters which are computed in an optimal way by solving a standard quadratic optimization problem maximizing Harrell's C-index. Numerical examples with real data illustrate the outperformance of the proposed model in comparison with the original random survival forest.

We show tight convergence rate bounds for gradient descent and MM algorithms for maximum likelihood estimation and maximum aposteriori probability estimation of a popular Bayesian inference method for generalized Bradley-Terry models. This class of models includes the Bradley-Terry model of paired comparisons, the Rao-Kupper model of paired comparisons with ties, the Luce choice model, and the Plackett-Luce ranking model. Our results show that MM algorithms have same convergence rates as gradient descent algorithms up to constant factors. For the maximum likelihood estimation, the convergence is linear with the rate crucially determined by the algebraic connectivity of the matrix of item pair co-occurrences in observed comparison data. For the Bayesian inference, the convergence rate is also linear, with the rate determined by a parameter of the prior distribution in a way that can make convergence arbitrarily slow for small values of this parameter. We propose a simple, first-order acceleration method that resolves the slow convergence issue.

The constant evolution of technology has meant data and information is being generated at a rate unlike ever before, and it's only on the rise. Furthermore, the demand for people skilled in analyzing, interpreting and using this data is already high and is set to grow exponentially over the coming years. These new roles cover all aspect from strategy, operations to governance. Hence, the current and future demand will require more data scientists, data engineers, data strategists, and Chief Data Officers. In this blog, we will be looking at different set of interview questions that can certainly help if you are planning to give a shift to your career towards data science.

There is a huge growth in machine learning development in the past few months. It is due to the availability of various open source tools that can create applications easily.- While the Python programming language feeds most machine learning frameworks, JavaScript has not lagged behind. This is the reason why JavaScript developers are using a number of frameworks for training and implementing machine learning models in the browser. In this blog, we will discuss various top machine learning JavaScript frameworks that you must consider for your online business growth in 2019.

Gradient descent is the most commonly used optimization method deployed in machine learning and deep learning algorithms. It's used to train a machine learning model and is based on a convex function. It does this to minimize a given cost function to its local minimum. Gradient descent was invented by French mathematician Louis Augustin Cauchy in 1847. Most machine learning and deep learning algorithms involve some sort of optimization. Optimization refers to the process of either minimizing or maximizing some function by altering its parameters.

Multichannel blind deconvolution is the problem of recovering an unknown signal $f$ and multiple unknown channels $x_i$ from convolutional measurements $y_i=x_i \circledast f$ ($i=1,2,\dots,N$). We consider the case where the $x_i$'s are sparse, and convolution with $f$ is invertible. Our nonconvex optimization formulation solves for a filter $h$ on the unit sphere that produces sparse output $y_i\circledast h$. Under some technical assumptions, we show that all local minima of the objective function correspond to the inverse filter of $f$ up to an inherent sign and shift ambiguity, and all saddle points have strictly negative curvatures. This geometric structure allows successful recovery of $f$ and $x_i$ using a simple manifold gradient descent algorithm with random initialization. Our theoretical findings are complemented by numerical experiments, which demonstrate superior performance of the proposed approach over the previous methods.

Asynchronous momentum stochastic gradient descent algorithms (Async-MSGD) have been widely used in distributed machine learning, e.g., training large collaborative filtering systems and deep neural networks. Due to current technical limit, however, establishing convergence properties of Async-MSGD for these highly complicated nonoconvex problems is generally infeasible. Therefore, we propose to analyze the algorithm through a simpler but nontrivial nonconvex problems --- streaming PCA. This allows us to make progress toward understanding Aync-MSGD and gaining new insights for more general problems. Specifically, by exploiting the diffusion approximation of stochastic optimization, we establish the asymptotic rate of convergence of Async-MSGD for streaming PCA. Our results indicate a fundamental tradeoff between asynchrony and momentum: To ensure convergence and acceleration through asynchrony, we have to reduce the momentum (compared with Sync-MSGD). To the best of our knowledge, this is the first theoretical attempt on understanding Async-MSGD for distributed nonconvex stochastic optimization. Numerical experiments on both streaming PCA and training deep neural networks are provided to support our findings for Async-MSGD.

Multichannel blind deconvolution is the problem of recovering an unknown signal $f$ and multiple unknown channels $x_i$ from convolutional measurements $y_i=x_i \circledast f$ ($i=1,2,\dots,N$). We consider the case where the $x_i$'s are sparse, and convolution with $f$ is invertible. Our nonconvex optimization formulation solves for a filter $h$ on the unit sphere that produces sparse output $y_i\circledast h$. Under some technical assumptions, we show that all local minima of the objective function correspond to the inverse filter of $f$ up to an inherent sign and shift ambiguity, and all saddle points have strictly negative curvatures. This geometric structure allows successful recovery of $f$ and $x_i$ using a simple manifold gradient descent algorithm with random initialization. Our theoretical findings are complemented by numerical experiments, which demonstrate superior performance of the proposed approach over the previous methods.