Active Learning is one of the teaching strategies which engage learners (e.g. Compared to the traditional learning process, learners do not just sit and listen but work together with teachers interactively. Progress of learning can be adjusted according to the feedback from learners. Therefore, the cycle of active learning is very important. If you are not familiar with active learning, you may visit this post.

During the Covid-19 pandemic, many educational institutions have been forced to provide home schooling. This includes alternative examination methods for schools and universities. A traditional exam is written in person under permanent surveillance of educational staff. However, online teaching and examinations can fail to ensure a proper surveillance of students. Different online proctoring methods are already used to make plagiarism or examination fraud more difficult.

In September 2018, I published a blog about my forthcoming book on The Mathematical Foundations of Data Science. The central question we address is: How can we bridge the gap between mathematics needed for Artificial Intelligence (Deep Learning and Machine learning) with that taught in high schools (up to ages 17/18)? In this post, we present a chapter from this book called "A Taxonomy of Machine Learning Models." The book is now available for an early bird discount released as chapters. If you are interested in getting early discounted copies, please contact ajit.jaokar at feynlabs.ai.

The term time-series analysis (TSA) refers to the statistical approach to time-series or the analysis of trend and seasonality. It is often an ad hoc exploration and analysis that usually involves visualizing distributions, trends, cyclic patterns, and relationships between features, and between features and the target(s). More generally, we can say TSA is roughly exploratory data analysis (EDA) that's specific to time-series data. This comparison can be misleading however since TSA can include both descriptive and exploratory elements. Let's see quickly the differences between descriptive and exploratory analysis: Therefore, TSA is the initial investigation of a dataset with the goal of discovering patterns, especially trend and seasonality, and obtaining initial insights, testing hypotheses, and extracting meaningful summary statistics.

We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and then iteratively refines estimates both on graph clustering and matrix ratings. Under a hierarchical stochastic block model that well respects practically-relevant social graphs and a low-rank rating matrix model (to be detailed), we demonstrate that our algorithm achieves the information-theoretic limit on the number of observed matrix entries (i.e., optimal sample complexity) that is derived by maximum likelihood estimation together with a lower-bound impossibility result. One consequence of this result is that exploiting the hierarchical structure of social graphs yields a substantial gain in sample complexity relative to the one that simply identifies different groups without resorting to the relational structure across them. We conduct extensive experiments both on synthetic and real-world datasets to corroborate our theoretical results as well as to demonstrate significant performance improvements over other matrix completion algorithms that leverage graph side information.

Bayesian optimization (BO) is a framework for global optimization of expensive-to-evaluate objective functions. Classical BO methods assume that the objective function is a black box. However, internal information about objective function computation is often available. For example, when optimizing a manufacturing line's throughput with simulation, we observe the number of parts waiting at each workstation, in addition to the overall throughput. Recent BO methods leverage such internal information to dramatically improve performance. We call these "grey-box" BO methods because they treat objective computation as partially observable and even modifiable, blending the black-box approach with so-called "white-box" first-principles knowledge of objective function computation. This tutorial describes these methods, focusing on BO of composite objective functions, where one can observe and selectively evaluate individual constituents that feed into the overall objective; and multi-fidelity BO, where one can evaluate cheaper approximations of the objective function by varying parameters of the evaluation oracle.

Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.

Study of reinforcement learning algorithms for sequential learning-based decision-making in unknown linear systems has become increasingly popular in the recent years. In the canonical version of the problem, the true dynamics matrices of the plant are unknown, and the goal consists of adaptive design of the control input for minimizing deviations from optimal policy. Still, the control actions must be diverse enough to lead to accurate identification of the unknown parameters [1]. The existing literature is notably rich, including adaptive policies based on optimistic approximations of the dynamics matrices over a confidence region [2, 3], as well as plugin estimates of unknown parameters after leveraging a dither signal [4, 5, 6], Bayesian approaches [7, 8, 9], and statistical bootstrap [10]. An important problem in in different areas of control theory is that of stabilization.

Machine learning is gradually being widely used in predicting acute pancreatitis. No study has classified or summarised various prediction tasks for acute pancreatitis. The performance of models in different studies and the problems associated with model construction remain unclear. Machine learning-based models have great predictive performance, and outperform conventional statistical models and clinical scores in some prediction tasks for acute pancreatitis. The IJMEDI checklist is a new quality assessment tool, and scores can be attempted to be associated with it to evaluate the effects and reliability of machine learning-based models.

Multinomial Logit (MNL) is one of the most popular discrete choice models and has been widely used to model ranking data. However, there is a long-standing technical challenge of learning MNL from many real-world ranking data: exact calculation of the MNL likelihood of \emph{partial rankings} is generally intractable. In this work, we develop a scalable method for approximating the MNL likelihood of general partial rankings in polynomial time complexity. We also extend the proposed method to learn mixture of MNL. We demonstrate that the proposed methods are particularly helpful for applications to choice-based network formation modeling, where the formation of new edges in a network is viewed as individuals making choices of their friends over a candidate set. The problem of learning mixture of MNL models from partial rankings naturally arises in such applications. And the proposed methods can be used to learn MNL models from network data without the strong assumption that temporal orders of all the edge formation are available. We conduct experiments on both synthetic and real-world network data to demonstrate that the proposed methods achieve more accurate parameter estimation and better fitness of data compared to conventional methods.