We design and analyze an algorithm for first-order stochastic optimization of a large class of functions on $\mathbb{R}^d$. In particular, we consider the \emph{variationally coherent} functions which can be convex or non-convex. The iterates of our algorithm on variationally coherent functions converge almost surely to the global minimizer $\boldsymbol{x}^*$. Additionally, the very same algorithm with the same hyperparameters, after $T$ iterations guarantees on convex functions that the expected suboptimality gap is bounded by $\widetilde{O}(\|\boldsymbol{x}^* - \boldsymbol{x}_0\| T^{-1/2+\epsilon})$ for any $\epsilon>0$. It is the first algorithm to achieve both these properties at the same time. Also, the rate for convex functions essentially matches the performance of parameter-free algorithms. Our algorithm is an instance of the Follow The Regularized Leader algorithm with the added twist of using \emph{rescaled gradients} and time-varying linearithmic regularizers.

The field of Natural language processing can be formally defined as - "A theoretically motivated range of computational techniques for analyzing and representing naturally occurring texts at one or more levels of linguistic analysis for the purpose of achieving human-like language processing for a range of tasks or applications"[69]. The naturally occurring text can be in written or spoken form.A wide array of domains contribute to NLP development like linguistics, computer science and psychology.The linguistics field helps to understand the formal structure of language while computer science domain helps to find efficient internal representations and data structures.The study of "Psychology" can be useful to understand the methodology used by humans for dealing with languages. NLP can be considered to be having two distinct focus namely (1)Natural Language Generation(NLG) and (2)Natural Language Understanding(NLU). The NLG deals with planning to use the representation of language to decide what should be generated at each point in interaction, while NLU needs to analyze language and decide which is best way to represent it meaningfully.We, in this survey paper, concentrate on area of NLU for written text.Hence the NLP henceforth might be considered as NLU and vice versa. Motivation for designing Indian NLP systems Hindi and English are the official languages in central government of India(GOI). Indian community faces a "Digital Divide" due to dominance of English as mode of communication in higher education, judiciary, corporate sector and Public administration at Central level whereas the government in states work in their respective regional languages [67].The expansion of Internet has inter-connected the socioeconomic environment of the world and redefined the concept of global culture.As per a report in 2017 by the companies kpmg and Google

We prove a universal approximation property (UAP) for a class of ODENet and a class of ResNet, which are used in many deep learning algorithms. The UAP can be stated as follows. Let $n$ and $m$ be the dimension of input and output data, and assume $m\leq n$. Then we show that ODENet width $n+m$ with any non-polynomial continuous activation function can approximate any continuous function on a compact subset on $\mathbb{R}^n$. We also show that ResNet has the same property as the depth tends to infinity. Furthermore, we derive explicitly the gradient of a loss function with respect to a certain tuning variable. We use this to construct a learning algorithm for ODENet. To demonstrate the usefulness of this algorithm, we apply it to a regression problem, a binary classification, and a multinomial classification in MNIST.

Clustering is one of the major techniques used for statistical data analysis. As the term suggests, "clustering" is defined as the process of gathering similar objects into different groups or distribution of datasets into subsets with a defined distance measure. K-means clustering is touted as a foundational algorithm every data scientist ought to have in their toolbox. K-means and k-medoids are methods used in partitional clustering algorithms whose functionality works based on specifying an initial number of groups or, more precisely, iteratively by reallocation of objects among groups. The algorithm works by first segregating all the points into an already selected number of clusters.

A Machine Learning interview calls for a rigorous interview process where the candidates are judged on various aspects such as technical and programming skills, knowledge of methods and clarity of basic concepts. If you aspire to apply for machine learning jobs, it is crucial to know what kind of interview questions generally recruiters and hiring managers may ask. This is an attempt to help you crack the machine learning interviews at major product based companies and start-ups. Usually, machine learning interviews at major companies require a thorough knowledge of data structures and algorithms. In the upcoming series of articles, we shall start from the basics of concepts and build upon these concepts to solve major interview questions. Machine learning interviews comprise of many rounds, which begin with a screening test. This comprises solving questions either on the white-board, or solving it on online platforms like HackerRank, LeetCode etc. Here, we have compiled a list of ...

The current work is motivated by the need for robust statistical methods for precision medicine; as such, we address the need for statistical methods that provide actionable inference for a single unit at any point in time. We aim to learn an optimal, unknown choice of the controlled components of the design in order to optimize the expected outcome; with that, we adapt the randomization mechanism for future time-point experiments based on the data collected on the individual over time. Our results demonstrate that one can learn the optimal rule based on a single sample, and thereby adjust the design at any point t with valid inference for the mean target parameter. This work provides several contributions to the field of statistical precision medicine. First, we define a general class of averages of conditional causal parameters defined by the current context for the single unit time-series data. We define a nonparametric model for the probability distribution of the time-series under few assumptions, and aim to fully utilize the sequential randomization in the estimation procedure via the double robust structure of the efficient influence curve of the proposed target parameter. We present multiple exploration-exploitation strategies for assigning treatment, and methods for estimating the optimal rule. Lastly, we present the study of the data-adaptive inference on the mean under the optimal treatment rule, where the target parameter adapts over time in response to the observed context of the individual. Our target parameter is pathwise differentiable with an efficient influence function that is doubly robust - which makes it easier to estimate than previously proposed variations. We characterize the limit distribution of our estimator under a Donsker condition expressed in terms of a notion of bracketing entropy adapted to martingale settings.

Meta-learning has enabled learning statistical models that can be quickly adapted to new prediction tasks. Motivated by use-cases in personalized federated learning, we study the often overlooked aspect of the modern meta-learning algorithms -- their data efficiency. To shed more light on which methods are more efficient, we use techniques from algorithmic stability to derive bounds on the transfer risk that have important practical implications, indicating how much supervision is needed and how it must be allocated for each method to attain the desired level of generalization. Further, we introduce a new simple framework for evaluating meta-learning methods under a limit on the available supervision, conduct an empirical study of MAML, Reptile, and Protonets, and demonstrate the differences in the behavior of these methods on few-shot and federated learning benchmarks. Finally, we propose active meta-learning, which incorporates active data selection into learning-to-learn, leading to better performance of all methods in the limited supervision regime.

Imputation is a popular technique for handling missing data. We consider a nonparametric approach to imputation using the kernel ridge regression technique and propose consistent variance estimation. The proposed variance estimator is based on a linearization approach which employs the entropy method to estimate the density ratio. The root-n consistency of the imputation estimator is established when a Sobolev space is utilized in the kernel ridge regression imputation, which enables us to develop the proposed variance estimator. Synthetic data experiments are presented to confirm our theory.

Regularized kernel-based methods such as support vector machines (SVMs) typically depend on the underlying probability measure $\mathrm{P}$ (respectively an empirical measure $\mathrm{D}_n$ in applications) as well as on the regularization parameter $\lambda$ and the kernel $k$. Whereas classical statistical robustness only considers the effect of small perturbations in $\mathrm{P}$, the present paper investigates the influence of simultaneous slight variations in the whole triple $(\mathrm{P},\lambda,k)$, respectively $(\mathrm{D}_n,\lambda_n,k)$, on the resulting predictor. Existing results from the literature are considerably generalized and improved. In order to also make them applicable to big data, where regular SVMs suffer from their super-linear computational requirements, we show how our results can be transferred to the context of localized learning. Here, the effect of slight variations in the applied regionalization, which might for example stem from changes in $\mathrm{P}$ respectively $\mathrm{D}_n$, is considered as well.

High-dimensional graphical models are often estimated using regularization that is aimed at reducing the number of edges in a network. In this work, we show how even simpler networks can be produced by aggregating the nodes of the graphical model. We develop a new convex regularized method, called the tree-aggregated graphical lasso or tag-lasso, that estimates graphical models that are both edge-sparse and node-aggregated. The aggregation is performed in a data-driven fashion by leveraging side information in the form of a tree that encodes node similarity and facilitates the interpretation of the resulting aggregated nodes. We provide an efficient implementation of the tag-lasso by using the locally adaptive alternating direction method of multipliers and illustrate our proposal's practical advantages in simulation and in applications in finance and biology.