**Sufficient Dimension Reduction (SDR)**

In statistics, sufficient dimension reduction (SDR) is a paradigm for analyzing data that combines the ideas of dimension reduction with the concept of sufficiency. Dimension reduction has long been a primary goal of regression analysis. Given a response variable y and a p-dimensional predictor vector \textbf{x}, regression analysis aims to study the distribution of y|\textbf{x}, the conditional distribution of y given \textbf{x}. A dimension reduction is a function R(\textbf{x}) that maps \textbf{x} to a subset of \mathbb{R}^k, k < p, thereby reducing the dimension of \textbf{x}. For example, R(\textbf{x}) may be one or more linear combinations of \textbf{x}. A dimension reduction R(\textbf{x}) is said to be sufficient if the distribution of y|R(\textbf{x}) is the same as that of y|\textbf{x}. In other words, no information about the regression is lost in reducing the dimension of \textbf{x} if the reduction is sufficient. … **LexVec**

In this paper, we propose LexVec, a new method for generating distributed word representations that uses low-rank, weighted factorization of the Positive Point-wise Mutual Information matrix via stochastic gradient descent, employing a weighting scheme that assigns heavier penalties for errors on frequent co-occurrences while still accounting for negative co-occurrence. Evaluation on word similarity and analogy tasks shows that LexVec matches and often outperforms state-of-the-art methods on many of these tasks. … **Multi-Armed Bandit**

In probability theory, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is the problem a gambler faces at a row of slot machines, sometimes known as “one-armed bandits”, when deciding which machines to play, how many times to play each machine and in which order to play them. When played, each machine provides a random reward from a distribution specific to that machine. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. …

# If you did not already know

**22**
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Jul 2017

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