Gamma Processes, Stick-Breaking, and Variational Inference

While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own right. Current inference schemes for models involving the gamma process are restricted to MCMC-based methods, which limits their scalability. In this paper, we present a variational inference framework for models involving gamma process priors. Our approach is based on a novel stick-breaking constructive definition of the gamma process. We prove correctness of this stick-breaking process by using the characterization of the gamma process as a completely random measure (CRM), and we explicitly derive the rate measure of our construction using Poisson process machinery. We also derive error bounds on the truncation of the infinite process required for variational inference, similar to the truncation analyses for other nonparametric models based on the Dirichlet and beta processes. Our representation is then used to derive a variational inference algorithm for a particular Bayesian nonparametric latent structure formulation known as the infinite Gamma-Poisson model, where the latent variables are drawn from a gamma process prior with Poisson likelihoods. Finally, we present results for our algorithms on nonnegative matrix factorization tasks on document corpora, and show that we compare favorably to both sampling-based techniques and variational approaches based on beta-Bernoulli priors

A real-world retrospective evaluation of glycaemic control and weight loss in patients with type 2 diabetes mellitus treated with canagliflozin 100 mg and canagliflozin 300 mg in an Indian setting

Background. Canagliflozin is a sodium glucose co- -transporter 2 (SGLT2) inhibitor that improves glycaemia in patients with type 2 diabetes mellitus (T2DM) by enhancing urinary glucose excretion (UGE). Indian data regarding comparative efficacy of canagliflozin 300 mg over canagliflozin 100 mg in reduction of body weight are scanty. Objectives. To evaluate and compare the efficacy of canagliflozin 100 mg versus canagliflozin 300 mg regarding loss of body weight retrospectively, in patients with T2DM inadequately controlled with other antihypergycaemic agents (AHA) in a real world setting in India. Methods. T2DM patients inadequately controlled (HbA1c > 8.5%) with diet, exercise and AHA who were prescribed canagliflozin 100 mg (n = 62) or canagliflozin 300 mg (n = 36) once daily, between May 2016 to May 2019 and were followed for at least 20 weeks, are included in the analysis. Changes in blood pressure and glycaemic parameters and body weight are studied. Results. Results show that addition of canagliflozin 100 and 300 mg provided statistically significant improvements in glycaemic control associated with weight loss. However no superiority of canagliflozin 300 mg to canagliflozin 100 mg is established. Conclusion. The present study shows that addition of canagliflozin 300 mg has no advantage over canagliflozin 100 mg on body weight when added on existing therapy with other AHA

Deregulation of LIMD1-VHL-HIF-1α-VEGF pathway is associated with different stages of cervical cancer.

To understand the mechanism of cellular stress in basal-parabasal layers of normal cervical epithelium and during different stages of cervical carcinoma, we analyzed the alterations (expression/methylation/copy number variation/mutation) of HIF-1α and its associated genes LIMD1, VHL and VEGF in disease-free normal cervix (n = 9), adjacent normal cervix of tumors (n = 70), cervical intraepithelial neoplasia (CIN; n = 32), cancer of uterine cervix (CACX; n = 174) samples and two CACX cell lines. In basal-parabasal layers of normal cervical epithelium, LIMD1 showed high protein expression, while low protein expression of VHL was concordant with high expression of HIF-1α and VEGF irrespective of HPV-16 (human papillomavirus 16) infection. This was in concordance with the low promoter methylation of LIMD1 and high in VHL in the basal-parabasal layers of normal cervix. LIMD1 expression was significantly reduced while VHL expression was unchanged during different stages of cervical carcinoma. This was in concordance with their frequent methylation during different stages of this tumor. In different stages of cervical carcinoma, the expression pattern of HIF-1α and VEGF was high as seen in basal-parabasal layers and inversely correlated with the expression of LIMD1 and VHL. This was validated by demethylation experiments using 5-aza-2'-deoxycytidine in CACX cell lines. Additional deletion of LIMD1 and VHL in CIN/CACX provided an additional growth advantage during cervical carcinogenesis through reduced expression of genes and associated with poor prognosis of patients. Our data showed that overexpression of HIF-1α and its target gene VEGF in the basal-parabasal layers of normal cervix was due to frequent inactivation of VHL by its promoter methylation. This profile was maintained during different stages of cervical carcinoma with additional methylation/deletion of VHL and LIMD1.This work was supported by CSIR (Council of Scientific and Industrial Research, Government of India)-JRF/NET grant [File No.09/030(0059)/2010-EMR-I] to Mr. C.Chakraborty, grant [Sr. No. 2121130723] from UGC (University Grants Commission, Government of India) to Mr. Sudip Samadder, grant [SR/SO/HS-116/2007] from DST (Department of Science and Technology, Government of India) to Dr. C. K. Panda and grant [ No. 60(0111)/14/EMR-II of dt.03/11/2014] from CSIR (Council of Scientific and Industrial Research, Government of India) to Dr. C. K. Pand

Gamma Processes, Stick-Breaking, and Variational Inference

Abstract While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own right. Current inference schemes for models involving the gamma process are restricted to MCMC-based methods, which limits their scalability. In this paper, we present a variational inference framework for models involving gamma process priors. Our approach is based on a novel stick-breaking constructive definition of the gamma process. We prove correctness of this stick-breaking process by using the characterization of the gamma process as a completely random measure (CRM), and we explicitly derive the rate measure of our construction using Poisson process machinery. We also derive error bounds on the truncation of the infinite process required for variational inference, similar to the truncation analyses for other nonparametric models based on the Dirichlet and beta processes. Our representation is then used to derive a variational inference algorithm for a particular Bayesian nonparametric latent structure formulation known as the infinite Gamma-Poisson model, where the latent variables are drawn from a gamma process prior with Poisson likelihoods. Finally, we present results for our algorithm on nonnegative matrix factorization tasks on document corpora, and show that we compare favorably to both sampling-based techniques and variational approaches based on betaBernoulli priors, as well as a direct DP-based construction of the gamma process

Effect of Noise on Generalized Synchronization: An Experimental Perspective

Generalized synchronization between two different nonlinear systems under influence of noise is studied with the help of an electronic circuit and numerical experiment. In the present case, we have studied the phenomena of generalized synchronization between the Lorenz system and another nonlinear system (modified Lorenz) proposed in Ray et al. (2011, “On the Study of Chaotic Systems With Non-Horseshoe Template,” Frontier in the Study of Chaotic Dynamical Systems With Open Problems, Vol. 16, E. Zeraoulia and J. C. Sprott, eds., World Scientific, Singapore, pp. 85–103) from the perspective of electronic circuits and corresponding data collected digitally. Variations of the synchronization threshold with coupling (between driver and driven system) and noise intensity have been studied in detail. Later, experimental results are also proved numerically. It is shown that in certain cases, noise enhances generalized synchronization, and in another it destroys generalized synchronization. Numerical studies in the latter part have also proved results obtained experimentally.</jats:p

Robust Monte Carlo Sampling using Riemannian Nosé-Poincaré Hamiltonian Dynamics

Abstract We present a Monte Carlo sampler using a modified Nosé-Poincaré Hamiltonian along with Riemannian preconditioning. Hamiltonian Monte Carlo samplers allow better exploration of the state space as opposed to random walk-based methods, but, from a molecular dynamics perspective, may not necessarily provide samples from the canonical ensemble. Nosé-Hoover samplers rectify that shortcoming, but the resultant dynamics are not Hamiltonian. Furthermore, usage of these algorithms on large real-life datasets necessitates the use of stochastic gradients, which acts as another potentially destabilizing source of noise. In this work, we propose dynamics based on a modified Nosé-Poincaré Hamiltonian augmented with Riemannian manifold corrections. The resultant symplectic sampling algorithm samples from the canonical ensemble while using structural cues from the Riemannian preconditioning matrices to efficiently traverse the parameter space. We also propose a stochastic variant using additional terms in the Hamiltonian to correct for the noise from the stochastic gradients. We show strong performance of our algorithms on synthetic datasets and high-dimensional Poisson factor analysisbased topic modeling scenarios