Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regression

Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this paper, we first bring together various probabilistic inequalities for sums of independent random variables under much weaker exponential type (namely sub-Weibull) tail assumptions. These results extract a part sub-Gaussian tail behavior in finite samples, matching the asymptotics governed by the central limit theorem, and are compactly represented in terms of a new Orlicz quasi-norm - the Generalized Bernstein-Orlicz norm - that typifies such tail behaviors. We illustrate the usefulness of these inequalities through the analysis of four fundamental problems in HD statistics. In the first two problems, we study the rate of convergence of the sample covariance matrix in terms of the maximum elementwise norm and the maximum k-sub-matrix operator norm which are key quantities of interest in bootstrap, HD covariance matrix estimation and HD inference. The third example concerns the restricted eigenvalue condition, required in HD linear regression, which we verify for all sub-Weibull random vectors through a unified analysis, and also prove a more general result related to restricted strong convexity in the process. In the final example, we consider the Lasso estimator for linear regression and establish its rate of convergence under much weaker than usual tail assumptions (on the errors as well as the covariates), while also allowing for misspecified models and both fixed and random design. To our knowledge, these are the first such results for Lasso obtained in this generality. The common feature in all our results over all the examples is that the convergence rates under most exponential tails match the usual ones under sub-Gaussian assumptions.Comment: 64 pages; Revised version (discussions added and some results modified in Section 4, minor changes made throughout

Probabilistic Inference for Phrase-based Machine Translation: A Sampling Approach

Recent advances in statistical machine translation (SMT) have used dynamic programming (DP) based beam search methods for approximate inference within probabilistic translation models. Despite their success, these methods compromise the probabilistic interpretation of the underlying model thus limiting the application of probabilistically defined decision rules during training and decoding. As an alternative, in this thesis, we propose a novel Monte Carlo sampling approach for theoretically sound approximate probabilistic inference within these models. The distribution we are interested in is the conditional distribution of a log-linear translation model; however, often, there is no tractable way of computing the normalisation term of the model. Instead, a Gibbs sampling approach for phrase-based machine translation models is developed which obviates the need of computing this term yet produces samples from the required distribution. We establish that the sampler effectively explores the distribution defined by a phrase-based models by showing that it converges in a reasonable amount of time to the desired distribution, irrespective of initialisation. Empirical evidence is provided to confirm that the sampler can provide accurate estimates of expectations of functions of interest. The mix of high probability and low probability derivations obtained through sampling is shown to provide a more accurate estimate of expectations than merely using the n-most highly probable derivations. Subsequently, we show that the sampler provides a tractable solution for finding the maximum probability translation in the model. We also present a unified approach to approximating two additional intractable problems: minimum risk training and minimum Bayes risk decoding. Key to our approach is the use of the sampler which allows us to explore the entire probability distribution and maintain a strict probabilistic formulation through the translation pipeline. For these tasks, sampling allies the simplicity of n-best list approaches with the extended view of the distribution that lattice-based approaches benefit from, while avoiding the biases associated with beam search. Our approach is theoretically well-motivated and can give better and more stable results than current state of the art methods

APPLICATION OF INTELLIGENT GAME THEORY APPROACH IN COGNITIVE RADIO AD HOC NETWORKS

Cognitive Radio (CR) technology is imagined to solve the problems in Wireless Ad-hoc NETworks (WANET) resulting from the limited available spectrum and the inefficiency in the spectrum usage by exploiting the existing wireless spectrum opportunistically. Game theory is a process to analyze multi-person decision making situation, where each decision maker tries to maximize his own utility. In this paper, we illustrates how various interactions in Cognitive Radio Ad Hoc Network (CRAHN) can be modeled as a game. It also illustrates a problem with solution approach that uses intelligent game theory technique in CRAHN

CORRELATION OF ARTIFICIAL INTELLIGENCE TECHNIQUES WITH SOFT COMPUTING IN VARIOUS AREAS

Artificial Intelligence (AI) is a part of computer science concerned with designing intelligent computer systems that exhibit the characteristics used to associate with intelligence in human behavior. Basically, it define as a field that study and design of intelligent agents. Traditional AI approach deals with cognitive and biological models that imitate and describe human information processing skills. This processing skills help to perceive and interact with their environment. But in modern era developers can build system that assemble superior information processing needs of government and industry by choosing from large areas of mature technologies. Soft Computing (SC) is an added area of AI. It focused on the design of intelligent systems that process uncertain, imprecise and incomplete information. It applied in real world problems frequently to offer more robust, tractable and less costly solutions than those obtained by more conventional mathematical techniques. This paper reviews correlation of artificial intelligence techniques with soft computing in various areas

Bilateral phyllodes tumor of the breast in a young nulliparous woman

Cystosarcoma phyllodes is a rare breast tumor with incidence of 1% of all the mammary tumors. Bilateral occurrence is very rare. Median age of presentation is 40-50 years. We present a case of 24 years old nulliparous female with phyllodes tumour developing in both the breasts one after another with a gap of five years. Patient underwent simple mastectomy on both sides. Histopathology report confirmed benign variety of cystosarcoma phyllodes on both sides

Monte Carlo inference and maximization for phrase-based translation

Recent advances in statistical machine translation have used beam search for approximate NP-complete inference within probabilistic translation models. We present an alternative approach of sampling from the posterior distribution defined by a translation model. We define a novel Gibbs sampler for sampling translations given a source sentence and show that it effectively explores this posterior distribution. In doing so we overcome the limitations of heuristic beam search and obtain theoretically sound solutions to inference problems such as finding the maximum probability translation and minimum expected risk training and decoding.

Myths and misbelieves regarding COVID vaccines in India

Background: - COVID-19 is the most important public health problem of recent time. Many people require hospitalization after infection. COVID vaccination is the most effective way to prevent the disease. Due to extensive negative publicity through social media channels/platforms,significant number of individuals are not coming forward for vaccination. Therefore, study is needed to evaluate adverse effects associated with different vaccines available in India. Objectives: - To assess the adverse effects associated with COVID-19 vaccination and compare the side effect of two most commonly used COVID vaccines in India. Methods:- In the current report, a cross sectional study was conducted among beneficiaries of COVID-19 vaccines at the vaccination center of the LLRM Medical college, India. After institutional ethical clearance and informed consent, patients were asked about the symptoms they experienced after vaccination. A very simple random sampling approach was used to select beneficiaries. Information was collected on predesigned Google form and total 391 patients submitted the responses. Results:- Out of total respondents 77 % individuals reported one or more symptoms. Fever was reported to be most common problem (59.3%) followed by body ache (57.5%). Out of total beneficiaries, 68.3% experienced mild symptoms while 23% remain asymptomatic. Only few subjects reported moderate adverse effects (8.7%).  None of the respondent reported severe and serious adverse effect. Conclusions:- Vaccine associated adverse effects were found less than 3 days and of mild variety in most of the beneficiaries. There was no difference in adverse effect profile of two commonly used vaccines in India. People must come forward for vaccination in mass without fearing of adverse effects of vaccines