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### Efficient Inverse-Free Algorithms for Extreme Learning Machine Based on the Recursive Matrix Inverse and the Inverse LDL' Factorization

The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of a Hermitian matrix. Before that recursive algorithm was applied in [4], its improved version had been utilized in previous literatures [9], [10]. Accordingly from the improved recursive algorithm [9], [10], we deduce a more efficient inverse-free algorithm to update the regularized pseudo-inverse, from which we develop the proposed inverse-free ELM algorithm 1. Moreover, the proposed ELM algorithm 2 further reduces the computational complexity, which computes the output weights directly from the updated inverse, and avoids computing the regularized pseudoinverse. Lastly, instead of updating the inverse, the proposed ELM algorithm 3 updates the LDLT factor of the inverse by the inverse LDLT factorization [11], to avoid numerical instabilities after a very large number of iterations [12]. With respect to the existing ELM algorithm, the proposed ELM algorithms 1, 2 and 3 are expected to require only (8+3)/M , (8+1)/M and (8+1)/M of complexities, respectively, where M is the output node number. In the numerical experiments, the standard ELM, the existing inverse-free ELM algorithm and the proposed ELM algorithms 1, 2 and 3 achieve the same performance in regression and classification, while all the 3 proposed algorithms significantly accelerate the existing inverse-free ELM algorithm

### A kNN algorithm with a unfixed k? • /r/MachineLearning

I am wondering if there is any research out their about an kNN classifier with a optimized algorithm where a function is trained upon the training data set that maps a point to a value of k. Then, when the algorithm needs to classify a new point, it first looks for the nearest point in this trained function to find what value k it should use. Any thoughts or links to research like this?

### Extending Gossip Algorithms to Distributed Estimation of U-statistics

Efficient and robust algorithms for decentralized estimation in networks are essential to many distributed systems. Whereas distributed estimation of sample mean statistics has been the subject of a good deal of attention, computation of U-statistics, relying on more expensive averaging over pairs of observations, is a less investigated area. Yet, such data functionals are essential to describe global properties of a statistical population, with important examples including Area Under the Curve, empirical variance, Gini mean difference and within-cluster point scatter. This paper proposes new synchronous and asynchronous randomized gossip algorithms which simultaneously propagate data across the network and maintain local estimates of the U-statistic of interest. We establish convergence rate bounds of O(1 / t) and O(log t / t) for the synchronous and asynchronous cases respectively, where t is the number of iterations, with explicit data and network dependent terms.

### Deterministic Single-Pass Algorithm for LDA

We develop a deterministic single-pass algorithm for latent Dirichlet allocation (LDA) in order to process received documents one at a time and then discard them in an excess text stream. Our algorithm does not need to store old statistics for all data. The proposed algorithm is much faster than a batch algorithm and is comparable to the batch algorithm in terms of perplexity in experiments. Papers published at the Neural Information Processing Systems Conference.

### Join-Graph Propagation Algorithms

The paper investigates parameterized approximate message-passing schemes that are based on bounded inference and are inspired by Pearls belief propagation algorithm (BP). We start with the bounded inference mini-clustering algorithm and then move to the iterative scheme called Iterative Join-Graph Propagation (IJGP), that combines both iteration and bounded inference. Algorithm IJGP belongs to the class of Generalized Belief Propagation algorithms, a framework that allowed connections with approximate algorithms from statistical physics and is shown empirically to surpass the performance of mini-clustering and belief propagation, as well as a number of other state-of-the-art algorithms on several classes of networks. We also provide insight into the accuracy of iterative BP and IJGP by relating these algorithms to well known classes of constraint propagation schemes.