By now, all of us have seen the results of various basic machine learning (ML) models. The internet is rife with images, videos, and articles showing off how a computer identifies, correctly or not, various animals. While we have moved towards more intricate machine learning models, such as ones that generate or upscale images, those basic ones still form the foundation of those efforts. Mastering the basics can become a launchpad for much greater future endeavors. So, I decided to revisit the basics myself and build a basic machine learning model with several caveats -- it must be somewhat useful, as simplistic as possible, and return reasonably accurate results. Unlike many other tutorials on the internet, however, I want to present my entire thought process from beginning to end. As such, the coding part will begin quite a bit later as problem selection in both the theoretical and practical realm is equally important. In the end, I believe that understanding why will go further than how to. Although machine learning can solve a great deal of challenges, it's not a one-size-fits-all approach. Even if we were to temporarily forget about the financial, temporal, and other resource costs, ML models would still be great at some things and terrible at others. Categorization is a great example of where machine learning may shine.

Here, I'll be giving an overview and theoretical concepts of the statistical learning. Supervised learning can play a key role in learning from examples. From this algorithm, useful information can be easily extracted from large datasets, the problem of learning from examples consecutively involves approximating functions from a sparse and noisy data. In supervised learning, network is trained on a dataset of the form, T {xk, dk} from k 1 to Q. It is observed that using MLP multilayer perceptron with sufficient number of hidden neurons, it is possible to approximate a given function to any arbitrary degree of accuracy.

"We have 60 churn models in production." I asked them why so many. They replied that they own 5 brands operating in 12 countries and, since they wanted to develop one model for each combination of brand and country, that amounts to 60 models. "Did you try with just 1 model?" They argued that it wouldn't make sense because their brands are very different from each other, and so are the countries they operate in: "You cannot train one single model and expect it to work well both on an American customer of brand A and on a German customer of brand B".

In this paper, we study a sequential decision-making problem, called Adaptive Sampling for Discovery (ASD). Starting with a large unlabeled dataset, algorithms for ASD adaptively label the points with the goal to maximize the sum of responses. This problem has wide applications to real-world discovery problems, for example drug discovery with the help of machine learning models. ASD algorithms face the well-known exploration-exploitation dilemma. The algorithm needs to choose points that yield information to improve model estimates but it also needs to exploit the model. We rigorously formulate the problem and propose a general information-directed sampling (IDS) algorithm. We provide theoretical guarantees for the performance of IDS in linear, graph and low-rank models. The benefits of IDS are shown in both simulation experiments and real-data experiments for discovering chemical reaction conditions.

Rankings are widely collected in various real-life scenarios, leading to the leakage of personal information such as users' preferences on videos or news. To protect rankings, existing works mainly develop privacy protection on a single ranking within a set of ranking or pairwise comparisons of a ranking under the $\epsilon$-differential privacy. This paper proposes a novel notion called $\epsilon$-ranking differential privacy for protecting ranks. We establish the connection between the Mallows model (Mallows, 1957) and the proposed $\epsilon$-ranking differential privacy. This allows us to develop a multistage ranking algorithm to generate synthetic rankings while satisfying the developed $\epsilon$-ranking differential privacy. Theoretical results regarding the utility of synthetic rankings in the downstream tasks, including the inference attack and the personalized ranking tasks, are established. For the inference attack, we quantify how $\epsilon$ affects the estimation of the true ranking based on synthetic rankings. For the personalized ranking task, we consider varying privacy preferences among users and quantify how their privacy preferences affect the consistency in estimating the optimal ranking function. Extensive numerical experiments are carried out to verify the theoretical results and demonstrate the effectiveness of the proposed synthetic ranking algorithm.

Non-linear state-space models, also known as general hidden Markov models, are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences in general. The particle-based, rapid incremental smoother PaRIS is a sequential Monte Carlo (SMC) technique allowing for efficient online approximation of expectations of additive functionals under the smoothing distribution in these models. Such expectations appear naturally in several learning contexts, such as likelihood estimation (MLE) and Markov score climbing (MSC). PARIS has linear computational complexity, limited memory requirements and comes with non-asymptotic bounds, convergence results and stability guarantees. Still, being based on self-normalised importance sampling, the PaRIS estimator is biased. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs PPG sampler, which can be viewed as a PaRIS algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. Our second contribution is to apply PPG in a learning framework, covering MLE and MSC as special examples. In this context, we establish, under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao--Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.

Matrix Factorization (MF) on large scale data takes substantial time on a Central Processing Unit (CPU). While Graphical Processing Unit (GPU)s could expedite the computation of MF, the available memory on a GPU is finite. Leveraging GPUs require alternative techniques that allow not only parallelism but also address memory limitations. Synchronization between computation units, isolation of data related to a computational unit, sharing of data between computational units and identification of independent tasks among computational units are some of the challenges while leveraging GPUs for MF. We propose a block based approach to matrix factorization using Stochastic Gradient Descent (SGD) that is aimed at accelerating MF on GPUs. The primary motivation for the approach is to make it viable to factorize extremely large data sets on limited hardware without having to compromise on results. The approach addresses factorization of large scale data by identifying independent blocks, each of which are factorized in parallel using multiple computational units. The approach can be extended to one or more GPUs and even to distributed systems. The RMSE results of the block based approach are with in acceptable delta in comparison to the results of CPU based variant and multi-threaded CPU variant of similar SGD kernel implementation. The advantage, of the block based variant, in-terms of speed are significant in comparison to other variants.

With Twitter's growth and popularity, a huge number of views are shared by users on various topics, making this platform a valuable information source on various political, social, and economic issues. This paper investigates English tweets on the Russia-Ukraine war to analyze trends reflecting users' opinions and sentiments regarding the conflict. The tweets' positive and negative sentiments are analyzed using a BERT-based model, and the time series associated with the frequency of positive and negative tweets for various countries is calculated. Then, we propose a method based on the neighborhood average for modeling and clustering the time series of countries. The clustering results provide valuable insight into public opinion regarding this conflict. Among other things, we can mention the similar thoughts of users from the United States, Canada, the United Kingdom, and most Western European countries versus the shared views of Eastern European, Scandinavian, Asian, and South American nations toward the conflict.

This article charts the work of a 4 month project aimed at automatically identifying patterns of tweets' popularity evolution using Machine Learning and Deep Learning techniques. To apprehend both the data and the extent of the problem, a straightforward clustering algorithm based on a point to point distance is used. Then, in an attempt to refine the algorithm, various analyses especially using feature extraction techniques are conducted. Although the algorithm eventually fails to automate such a task, this exercise raises a complex but necessary issue touching on the impact of virality on social networks.

In the paper, we study a class of useful minimax problems on Riemanian manifolds and propose a class of effective Riemanian gradient-based methods to solve these minimax problems. Specifically, we propose an effective Riemannian gradient descent ascent (RGDA) algorithm for the deterministic minimax optimization. Moreover, we prove that our RGDA has a sample complexity of $O(\kappa^2\epsilon^{-2})$ for finding an $\epsilon$-stationary solution of the Geodesically-Nonconvex Strongly-Concave (GNSC) minimax problems, where $\kappa$ denotes the condition number. At the same time, we present an effective Riemannian stochastic gradient descent ascent (RSGDA) algorithm for the stochastic minimax optimization, which has a sample complexity of $O(\kappa^4\epsilon^{-4})$ for finding an $\epsilon$-stationary solution. To further reduce the sample complexity, we propose an accelerated Riemannian stochastic gradient descent ascent (Acc-RSGDA) algorithm based on the momentum-based variance-reduced technique. We prove that our Acc-RSGDA algorithm achieves a lower sample complexity of $\tilde{O}(\kappa^{4}\epsilon^{-3})$ in searching for an $\epsilon$-stationary solution of the GNSC minimax problems. Extensive experimental results on the robust distributional optimization and robust Deep Neural Networks (DNNs) training over Stiefel manifold demonstrate efficiency of our algorithms.