Unsupervised Representation Learning with Minimax Distance Measures

We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to employ Minimax distances with many machine learning methods that perform on numerical data. We study both computing the pairwise Minimax distances for all pairs of objects and as well as computing the Minimax distances of all the objects to/from a fixed (test) object. We first efficiently compute the pairwise Minimax distances between the objects, using the equivalence of Minimax distances over a graph and over a minimum spanning tree constructed on that. Then, we perform an embedding of the pairwise Minimax distances into a new vector space, such that their squared Euclidean distances in the new space equal to the pairwise Minimax distances in the original space. We also study the case of having multiple pairwise Minimax matrices, instead of a single one. Thereby, we propose an embedding via first summing up the centered matrices and then performing an eigenvalue decomposition to obtain the relevant features. In the following, we study computing Minimax distances from a fixed (test) object which can be used for instance in K-nearest neighbor search. Similar to the case of all-pair pairwise Minimax distances, we develop an efficient and general-purpose algorithm that is applicable with any arbitrary base distance measure. Moreover, we investigate in detail the edges selected by the Minimax distances and thereby explore the ability of Minimax distances in detecting outlier objects. Finally, for each setting, we perform several experiments to demonstrate the effectiveness of our framework.Comment: 32 page

LambdaFM: Learning Optimal Ranking with Factorization Machines Using Lambda Surrogates

State-of-the-art item recommendation algorithms, which apply Factorization Machines (FM) as a scoring function and pairwise ranking loss as a trainer (PRFM for short), have been recently investigated for the implicit feedback based context-aware recommendation problem (IFCAR). However, good recommenders particularly emphasize on the accuracy near the top of the ranked list, and typical pairwise loss functions might not match well with such a requirement. In this paper, we demonstrate, both theoretically and empirically, PRFM models usually lead to non-optimal item recommendation results due to such a mismatch. Inspired by the success of LambdaRank, we introduce Lambda Factorization Machines (LambdaFM), which is particularly intended for optimizing ranking performance for IFCAR. We also point out that the original lambda function suffers from the issue of expensive computational complexity in such settings due to a large amount of unobserved feedback. Hence, instead of directly adopting the original lambda strategy, we create three effective lambda surrogates by conducting a theoretical analysis for lambda from the top-N optimization perspective. Further, we prove that the proposed lambda surrogates are generic and applicable to a large set of pairwise ranking loss functions. Experimental results demonstrate LambdaFM significantly outperforms state-of-the-art algorithms on three real-world datasets in terms of four standard ranking measures

Second-generation PLINK: rising to the challenge of larger and richer datasets

PLINK 1 is a widely used open-source C/C++ toolset for genome-wide association studies (GWAS) and research in population genetics. However, the steady accumulation of data from imputation and whole-genome sequencing studies has exposed a strong need for even faster and more scalable implementations of key functions. In addition, GWAS and population-genetic data now frequently contain probabilistic calls, phase information, and/or multiallelic variants, none of which can be represented by PLINK 1's primary data format. To address these issues, we are developing a second-generation codebase for PLINK. The first major release from this codebase, PLINK 1.9, introduces extensive use of bit-level parallelism, O(sqrt(n))-time/constant-space Hardy-Weinberg equilibrium and Fisher's exact tests, and many other algorithmic improvements. In combination, these changes accelerate most operations by 1-4 orders of magnitude, and allow the program to handle datasets too large to fit in RAM. This will be followed by PLINK 2.0, which will introduce (a) a new data format capable of efficiently representing probabilities, phase, and multiallelic variants, and (b) extensions of many functions to account for the new types of information. The second-generation versions of PLINK will offer dramatic improvements in performance and compatibility. For the first time, users without access to high-end computing resources can perform several essential analyses of the feature-rich and very large genetic datasets coming into use.Comment: 2 figures, 1 additional fil