The stock market offers a platform where people buy and sell shares of publicly listed companies. Generally, stock prices are quite volatile; hence predicting them is a daunting task. There is still much research going to develop more accuracy in stock price prediction. Portfolio construction refers to the allocation of different sector stocks optimally to achieve a maximum return by taking a minimum risk. A good portfolio can help investors earn maximum profit by taking a minimum risk. Beginning with Dow Jones Theory a lot of advancement has happened in the area of building efficient portfolios. In this project, we have tried to predict the future value of a few stocks from six important sectors of the Indian economy and also built a portfolio. As part of the project, our team has conducted a study of the performance of various Time series, machine learning, and deep learning models in stock price prediction on selected stocks from the chosen six important sectors of the economy. As part of building an efficient portfolio, we have studied multiple portfolio optimization theories beginning with the Modern Portfolio theory. We have built a minimum variance portfolio and optimal risk portfolio for all the six chosen sectors by using the daily stock prices over the past five years as training data and have also conducted back testing to check the performance of the portfolio. We look forward to continuing our study in the area of stock price prediction and asset allocation and consider this project as the first stepping stone.

Electronic health records (EHRs) offer great promises for advancing precision medicine and, at the same time, present significant analytical challenges. Particularly, it is often the case that patient-level data in EHRs cannot be shared across institutions (data sources) due to government regulations and/or institutional policies. As a result, there are growing interests about distributed learning over multiple EHRs databases without sharing patient-level data. To tackle such challenges, we propose a novel communication efficient method that aggregates the local optimal estimates, by turning the problem into a missing data problem. In addition, we propose incorporating posterior samples of remote sites, which can provide partial information on the missing quantities and improve efficiency of parameter estimates while having the differential privacy property and thus reducing the risk of information leaking. The proposed approach, without sharing the raw patient level data, allows for proper statistical inference and can accommodate sparse regressions. We provide theoretical investigation for the asymptotic properties of the proposed method for statistical inference as well as differential privacy, and evaluate its performance in simulations and real data analyses in comparison with several recently developed methods.

Inductive Conformal Prediction (ICP) is a set of distribution-free and model agnostic algorithms devised to predict with a user-defined confidence with coverage guarantee. Instead of having point predictions, i.e., a real number in the case of regression or a single class in multi class classification, models calibrated using ICP output an interval or a set of classes, respectively. ICP takes special importance in high-risk settings where we want the true output to belong to the prediction set with high probability. As an example, a classification model might output that given a magnetic resonance image a patient has no latent diseases to report. However, this model output was based on the most likely class, the second most likely class might tell that the patient has a 15% chance of brain tumor or other severe disease and therefore further exams should be conducted. Using ICP is therefore way more informative and we believe that should be the standard way of producing forecasts. This paper is a hands-on introduction, this means that we will provide examples as we introduce the theory.

A determinantal point process (DPP) is an elegant model that assigns a probability to every subset of a collection of $n$ items. While conventionally a DPP is parameterized by a symmetric kernel matrix, removing this symmetry constraint, resulting in nonsymmetric DPPs (NDPPs), leads to significant improvements in modeling power and predictive performance. Recent work has studied an approximate Markov chain Monte Carlo (MCMC) sampling algorithm for NDPPs restricted to size-$k$ subsets (called $k$-NDPPs). However, the runtime of this approach is quadratic in $n$, making it infeasible for large-scale settings. In this work, we develop a scalable MCMC sampling algorithm for $k$-NDPPs with low-rank kernels, thus enabling runtime that is sublinear in $n$. Our method is based on a state-of-the-art NDPP rejection sampling algorithm, which we enhance with a novel approach for efficiently constructing the proposal distribution. Furthermore, we extend our scalable $k$-NDPP sampling algorithm to NDPPs without size constraints. Our resulting sampling method has polynomial time complexity in the rank of the kernel, while the existing approach has runtime that is exponential in the rank. With both a theoretical analysis and experiments on real-world datasets, we verify that our scalable approximate sampling algorithms are orders of magnitude faster than existing sampling approaches for $k$-NDPPs and NDPPs.

Federated learning (FL) is an emerging machine learning paradigm involving multiple clients, e.g., mobile phone devices, with an incentive to collaborate in solving a machine learning problem coordinated by a central server. FL was proposed in 2016 by Kone\v{c}n\'{y} et al. and McMahan et al. as a viable privacy-preserving alternative to traditional centralized machine learning since, by construction, the training data points are decentralized and never transferred by the clients to a central server. Therefore, to a certain degree, FL mitigates the privacy risks associated with centralized data collection. Unfortunately, optimization for FL faces several specific issues that centralized optimization usually does not need to handle. In this thesis, we identify several of these challenges and propose new methods and algorithms to address them, with the ultimate goal of enabling practical FL solutions supported with mathematically rigorous guarantees.

We demonstrate the application of the YOLOv5 model, a general purpose convolution-based single-shot object detection model, in the task of detecting binary neutron star (BNS) coalescence events from gravitational-wave data of current generation interferometer detectors. We also present a thorough explanation of the synthetic data generation and preparation tasks based on approximant waveform models used for the model training, validation and testing steps. Using this approach, we achieve mean average precision ($\text{mAP}_{[0.50]}$) values of 0.945 for a single class validation dataset and as high as 0.978 for test datasets. Moreover, the trained model is successful in identifying the GW170817 event in the LIGO H1 detector data. The identification of this event is also possible for the LIGO L1 detector data with an additional pre-processing step, without the need of removing the large glitch in the final stages of the inspiral. The detection of the GW190425 event is less successful, which attests to performance degradation with the signal-to-noise ratio. Our study indicates that the YOLOv5 model is an interesting approach for first-stage detection alarm pipelines and, when integrated in more complex pipelines, for real-time inference of physical source parameters.

Machine learning is one of the artificial intelligence models frequently used for modeling, prediction, and management of swine farming. Machine learning models mainly include algorithms of a decision tree, clustering, a support vector machine, and the Markov chain model focused on disease detection, behaviour recognition for postural classification, and sound detection of animals. The researchers from North Carolina State University and Smithfield Premium Genetics* demonstrated the application of machine learning algorithms to estimate body weight in growing pigs from feeding behaviour and feed intake data. Feed intake, feeder occupation time, and body weight information were collected from 655 pigs of 3 breeds (Duroc, Landrace, and Large White) from 75 to 166 days of age. 2 machine learning algorithms (long short-term memory network and random forest) were selected to forecast the body weight of pigs using 4 scenarios. Long short-term memory was used to accurately predict time series data due to its ability in learning and storing long term patterns in a sequence-dependent order and random forest approach was used as a representative algorithm in the machine learning space.

N1 - UKRI Rights Retention: For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising Funding: DS acknowledges support from the EPSRC Programme Grant TRANSNET (EP/R035342/1) and the Leverhulme trust (RPG-2018-092). YR acknowledges support by the EPSRC Horizon Digital Economy Research grant'Trusted Data Driven Products: EP/T022493/1 and grant'From Human Data to Personal Experience': EP/M02315X/1. N2 - We introduce the underlying concepts which give rise to some of the commonly used machine learning methods, excluding deep-learning machines and neural networks. We point to their advantages, limitations and potential use in various areas of photonics. The main methods covered include parametric and non-parametric regression and classification techniques, kernel-based methods and support vector machines, decision trees, probabilistic models, Bayesian graphs, mixture models, Gaussian processes, message passing methods and visual informatics.

Significant theoretical work has established that in specific regimes, neural networks trained by gradient descent behave like kernel methods. However, in practice, it is known that neural networks strongly outperform their associated kernels. In this work, we explain this gap by demonstrating that there is a large class of functions which cannot be efficiently learned by kernel methods but can be easily learned with gradient descent on a two layer neural network outside the kernel regime by learning representations that are relevant to the target task. We also demonstrate that these representations allow for efficient transfer learning, which is impossible in the kernel regime. Specifically, we consider the problem of learning polynomials which depend on only a few relevant directions, i.e. of the form $f^\star(x) = g(Ux)$ where $U: \R^d \to \R^r$ with $d \gg r$. When the degree of $f^\star$ is $p$, it is known that $n \asymp d^p$ samples are necessary to learn $f^\star$ in the kernel regime. Our primary result is that gradient descent learns a representation of the data which depends only on the directions relevant to $f^\star$. This results in an improved sample complexity of $n\asymp d^2 r + dr^p$. Furthermore, in a transfer learning setup where the data distributions in the source and target domain share the same representation $U$ but have different polynomial heads we show that a popular heuristic for transfer learning has a target sample complexity independent of $d$.

We present an approach to clustering time series data using a model-based generalization of the K-Means algorithm which we call K-Models. We prove the convergence of this general algorithm and relate it to the hard-EM algorithm for mixture modeling. We then apply our method first with an AR($p$) clustering example and show how the clustering algorithm can be made robust to outliers using a least-absolute deviations criteria. We then build our clustering algorithm up for ARMA($p,q$) models and extend this to ARIMA($p,d,q$) models. We develop a goodness of fit statistic for the models fitted to clusters based on the Ljung-Box statistic. We perform experiments with simulated data to show how the algorithm can be used for outlier detection, detecting distributional drift, and discuss the impact of initialization method on empty clusters. We also perform experiments on real data which show that our method is competitive with other existing methods for similar time series clustering tasks.