Online Tensor Methods for Learning Latent Variable Models

We introduce an online tensor decomposition based approach for two latent variable modeling problems namely, (1) community detection, in which we learn the latent communities that the social actors in social networks belong to, and (2) topic modeling, in which we infer hidden topics of text articles. We consider decomposition of moment tensors using stochastic gradient descent. We conduct optimization of multilinear operations in SGD and avoid directly forming the tensors, to save computational and storage costs. We present optimized algorithm in two platforms. Our GPU-based implementation exploits the parallelism of SIMD architectures to allow for maximum speed-up by a careful optimization of storage and data transfer, whereas our CPU-based implementation uses efficient sparse matrix computations and is suitable for large sparse datasets. For the community detection problem, we demonstrate accuracy and computational efficiency on Facebook, Yelp and DBLP datasets, and for the topic modeling problem, we also demonstrate good performance on the New York Times dataset. We compare our results to the state-of-the-art algorithms such as the variational method, and report a gain of accuracy and a gain of several orders of magnitude in the execution time.Comment: JMLR 201

Tensor vs Matrix Methods: Robust Tensor Decomposition under Block Sparse Perturbations

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the residual. We prove convergence to the globally optimal solution under natural incoherence conditions on the low rank component, and bounded level of sparse perturbations. We compare our method with natural baselines which apply robust matrix PCA either to the {\em flattened} tensor, or to the matrix slices of the tensor. Our method can provably handle a far greater level of perturbation when the sparse tensor is block-structured. This naturally occurs in many applications such as the activity detection task in videos. Our experiments validate these findings. Thus, we establish that tensor methods can tolerate a higher level of gross corruptions compared to matrix methods

Tensor Contractions with Extended BLAS Kernels on CPU and GPU

Tensor contractions constitute a key computational ingredient of numerical multi-linear algebra. However, as the order and dimension of tensors grow, the time and space complexities of tensor-based computations grow quickly. In this paper, we propose and evaluate new BLAS-like primitives that are capable of performing a wide range of tensor contractions on CPU and GPU efficiently. We begin by focusing on single-index contractions involving all the possible configurations of second-order and third-order tensors. Then, we discuss extensions to more general cases. Existing approaches for tensor contractions spend large amounts of time restructuring the data which typically involves explicit copy and transpose operations. In this work, we summarize existing approaches and present library-based approaches that avoid memory movement. Through systematic benchmarking, we demonstrate that our approach can achieve 10x speedup on a K40c GPU and 2x speedup on dual-socket Haswell-EP CPUs, using MKL and CUBLAS respectively, for small and moderate tensor sizes. This is relevant in many machine learning applications such as deep learning, where tensor sizes tend to be small, but require numerous tensor contraction operations to be performed successively. Concretely, we implement a Tucker decomposition and show that using our kernels yields atleast an order of magnitude speedup as compared to state-of-the-art libraries

Does selection index application for highly heritable traits need revisiting – A comprehensive study with bodyweight and shank length in Vanaraja male line chicken

Selection index (SI) is one of the best methods for estimating the breeding value of an animal combining all sources of information on the animal and its relatives. In the present study, the SI was constructed utilizing the five generations data of Vanaraja male line (PD-1) for body weight (BW-6) and shank length (SL-6) at 6 weeks of age with variance, covariance estimates and heritability of both the traits. The SI was employed on three generations data on simulation basis and the selection parameters were estimated and compared with the mass selection (MS) actually practiced in the population. The least squares mean of SL-6, the primary trait of selection increased from 76.63±0.002 (G-I) to 82.85 ±0.002 mm (G-II), and subsequently reduced to 80.17±001 mm (G-III). The BW-6 also followed similar trend. Generation had significant effect on both SL-6 and BW-6. The heritability estimates for SL-6 and BW-6 were moderate with 0.21 to 0.28 for SL-6 and 0.22 to 0.27 for BW-6. The two traits exhibited high degree of positive association with 0.87 to 0.92 correlation coefficient. The economic value estimated for weight and shank length was 1:8.95. Thus, the selection index constructed was I= 0.2260*BW6, g + 0.7717*SL6, mm. Selection differential was higher in SI method on pooled basis compared to MS in all three generations for the primary trait, SL-6. The response to selection and selection intensity was also higher in SI method compared to MS. A similar trend was observed for BW-6 with respect to selection differential and response to selection. The study concluded that SI was superior to mass selection based on the results in Vanaraja male line chicken

Long-Term Programming of Antigen-Specific Immunity from Gene Expression Signatures in the PBMC of Rhesus Macaques Immunized with an SIV DNA Vaccine

While HIV-1-specific cellular immunity is thought to be critical for the suppression of viral replication, the correlates of protection have not yet been determined. Rhesus macaques (RM) are an important animal model for the study and development of vaccines against HIV/AIDS. Our laboratory has helped to develop and study DNA-based vaccines in which recent technological advances, including genetic optimization and in vivo electroporation (EP), have helped to dramatically boost their immunogenicity. In this study, RMs were immunized with a DNA vaccine including individual plasmids encoding SIV gag, env, and pol alone, or in combination with a molecular adjuvant, plasmid DNA expressing the chemokine ligand 5 (RANTES), followed by EP. Along with standard immunological assays, flow-based activation analysis without ex vivo restimulation and high-throughput gene expression analysis was performed. Strong cellular immunity was induced by vaccination which was supported by all assays including PBMC microarray analysis that identified the up-regulation of 563 gene sequences including those involved in interferon signaling. Furthermore, 699 gene sequences were differentially regulated in these groups at peak viremia following SIVmac251 challenge. We observed that the RANTES-adjuvanted animals were significantly better at suppressing viral replication during chronic infection and exhibited a distinct pattern of gene expression which included immune cell-trafficking and cell cycle genes. Furthermore, a greater percentage of vaccine-induced central memory CD8+ T-cells capable of an activated phenotype were detected in these animals as measured by activation analysis. Thus, co-immunization with the RANTES molecular adjuvant followed by EP led to the generation of cellular immunity that was transcriptionally distinct and had a greater protective efficacy than its DNA alone counterpart. Furthermore, activation analysis and high-throughput gene expression data may provide better insight into mechanisms of viral control than may be observed using standard immunological assays

Global economic burden of unmet surgical need for appendicitis

Background: There is a substantial gap in provision of adequate surgical care in many low-and middle-income countries. This study aimed to identify the economic burden of unmet surgical need for the common condition of appendicitis. Methods: Data on the incidence of appendicitis from 170 countries and two different approaches were used to estimate numbers of patients who do not receive surgery: as a fixed proportion of the total unmet surgical need per country (approach 1); and based on country income status (approach 2). Indirect costs with current levels of access and local quality, and those if quality were at the standards of high-income countries, were estimated. A human capital approach was applied, focusing on the economic burden resulting from premature death and absenteeism. Results: Excess mortality was 4185 per 100 000 cases of appendicitis using approach 1 and 3448 per 100 000 using approach 2. The economic burden of continuing current levels of access and local quality was US $92 492 million using approach 1 and$73 141 million using approach 2. The economic burden of not providing surgical care to the standards of high-income countries was $95 004 million using approach 1 and$75 666 million using approach 2. The largest share of these costs resulted from premature death (97.7 per cent) and lack of access (97.0 per cent) in contrast to lack of quality. Conclusion: For a comparatively non-complex emergency condition such as appendicitis, increasing access to care should be prioritized. Although improving quality of care should not be neglected, increasing provision of care at current standards could reduce societal costs substantially