Data Science is the buzzword, and a lot of enthusiasts are interested in learning its fundamentals to make a lucrative career in this field. Linear Algebra is one of the important concepts to learn how to perform data transformation techniques like pre-processing, dimensionality reduction, etc. There are many courses available at your fingertip, but it is difficult to choose the right course suited for your requirement. That's precisely the intent of this post - it makes your course search easy by listing down the five free courses to learn linear algebra foundations for data science. Before I go straight into listing down the courses for you, let me first explain the commonly asked questions – why do we need to learn linear algebra in the first place?

I'm happy to share that I've obtained a new certification: AWS Machine Learning Foundations from Udacity! One of the things I found interesting about this course is my recent exposure to and hands-on experience with generative AI. Generative AI gives the ability to create new 3d cad designs, and generate new data, algorithms, etc. from a pre-trained model. In the coming days, I will be exploring Generative AI in the design of robot components. Special appreciation to AWS amazon and Udacity for the privilege to participate in this program.

This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics. Wasserstein estimators are defined as solutions of variational problems whose objective function involves the use of an optimal transport cost between probability measures. Such estimators can be regularized by replacing the optimal transport cost by its regularized version using an entropy penalty on the transport plan. The use of such a regularization has a potentially significant smoothing effect on the resulting estimators. In this work, we investigate its potential benefits on the approximation and estimation properties of regularized Wasserstein estimators. Our main contribution is to discuss how entropic regularization may reach, at a lowest computational cost, statistical performances that are comparable to those of un-regularized Wasserstein estimators in statistical learning problems involving distributional data analysis. To this end, we present new theoretical results on the convergence of regularized Wasserstein estimators. We also study their numerical performances using simulated and real data in the supervised learning problem of proportions estimation in mixture models using optimal transport.

Most PAC-Bayesian bounds hold in the batch learning setting where data is collected at once, prior to inference or prediction. This somewhat departs from many contemporary learning problems where data streams are collected and the algorithms must dynamically adjust. We prove new PAC-Bayesian bounds in this online learning framework, leveraging an updated definition of regret, and we revisit classical PAC-Bayesian results with a batch-to-online conversion, extending their remit to the case of dependent data. Our results hold for bounded losses, potentially \emph{non-convex}, paving the way to promising developments in online learning.

In recent years, the role of big data analytics has exponentially grown and is now slowly making its way into the education industry. Several attempts are being made in this sphere in order to improve the quality of education being provided to students and while many collaborations have been carried out before, automated scoring of answers has been explored to a rather limited extent. One of the biggest hurdles to choosing constructed-response assessments over multiple-choice assessments is the effort and large cost that comes with their evaluation and this is precisely the issue that this project aims to solve. The aim is to accept raw-input from the student in the form of their answer, preprocess the answer, and automatically score the answer. In addition, we have made this a real-time system that captures "snapshots" of the writer's progress with respect to the answer, allowing us to unearth trends with respect to the way a student thinks, and how the student has arrived at their final answer.

Large-scale, high-quality corpora are critical for advancing research in coreference resolution. However, existing datasets vary in their definition of coreferences and have been collected via complex and lengthy guidelines that are curated for linguistic experts. These concerns have sparked a growing interest among researchers to curate a unified set of guidelines suitable for annotators with various backgrounds. In this work, we develop a crowdsourcing-friendly coreference annotation methodology, ezCoref, consisting of an annotation tool and an interactive tutorial. We use ezCoref to re-annotate 240 passages from seven existing English coreference datasets (spanning fiction, news, and multiple other domains) while teaching annotators only cases that are treated similarly across these datasets. Surprisingly, we find that reasonable quality annotations were already achievable (>90% agreement between the crowd and expert annotations) even without extensive training. On carefully analyzing the remaining disagreements, we identify the presence of linguistic cases that our annotators unanimously agree upon but lack unified treatments (e.g., generic pronouns, appositives) in existing datasets. We propose the research community should revisit these phenomena when curating future unified annotation guidelines.

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse problems. We find that state-of-the-art training techniques are not well-suited to many problems that involve physical processes. The highly nonlinear behavior, common in physical processes, results in strongly varying gradients that lead first-order optimizers like SGD or Adam to compute suboptimal optimization directions. We propose a novel hybrid training approach that combines higher-order optimization methods with machine learning techniques. We take updates from a scale-invariant inverse problem solver and embed them into the gradient-descent-based learning pipeline, replacing the regular gradient of the physical process. We demonstrate the capabilities of our method on a variety of canonical physical systems, showing that it yields significant improvements on a wide range of optimization and learning problems.

We study sequential bilateral trade where sellers and buyers valuations are completely arbitrary (i.e., determined by an adversary). Sellers and buyers are strategic agents with private valuations for the good and the goal is to design a mechanism that maximizes efficiency (or gain from trade) while being incentive compatible, individually rational and budget balanced. In this paper we consider gain from trade which is harder to approximate than social welfare. We consider a variety of feedback scenarios and distinguish the cases where the mechanism posts one price and when it can post different prices for buyer and seller. We show several surprising results about the separation between the different scenarios. In particular we show that (a) it is impossible to achieve sublinear $\alpha$-regret for any $\alpha<2$, (b) but with full feedback sublinear $2$-regret is achievable (c) with a single price and partial feedback one cannot get sublinear $\alpha$ regret for any constant $\alpha$ (d) nevertheless, posting two prices even with one-bit feedback achieves sublinear $2$-regret, and (e) there is a provable separation in the $2$-regret bounds between full and partial feedback.

The recent proliferation of NISQ devices has made it imperative to understand their computational power. In this work, we define and study the complexity class $\textsf{NISQ} $, which is intended to encapsulate problems that can be efficiently solved by a classical computer with access to a NISQ device. To model existing devices, we assume the device can (1) noisily initialize all qubits, (2) apply many noisy quantum gates, and (3) perform a noisy measurement on all qubits. We first give evidence that $\textsf{BPP}\subsetneq \textsf{NISQ}\subsetneq \textsf{BQP}$, by demonstrating super-polynomial oracle separations among the three classes, based on modifications of Simon's problem. We then consider the power of $\textsf{NISQ}$ for three well-studied problems. For unstructured search, we prove that $\textsf{NISQ}$ cannot achieve a Grover-like quadratic speedup over $\textsf{BPP}$. For the Bernstein-Vazirani problem, we show that $\textsf{NISQ}$ only needs a number of queries logarithmic in what is required for $\textsf{BPP}$. Finally, for a quantum state learning problem, we prove that $\textsf{NISQ}$ is exponentially weaker than classical computation with access to noiseless constant-depth quantum circuits.

Machine learning techniques rely on large and diverse datasets for generalization. Computer vision, natural language processing, and other applications can often reuse public datasets to train many different models. However, due to differences in physical configurations, it is challenging to leverage public datasets for training robotic control policies on new robot platforms or for new tasks. In this work, we propose a novel framework, ExAug to augment the experiences of different robot platforms from multiple datasets in diverse environments. ExAug leverages a simple principle: by extracting 3D information in the form of a point cloud, we can create much more complex and structured augmentations, utilizing both generating synthetic images and geometric-aware penalization that would have been suitable in the same situation for a different robot, with different size, turning radius, and camera placement. The trained policy is evaluated on two new robot platforms with three different cameras in indoor and outdoor environments with obstacles.