Archetypal analysis is an exploratory tool that explains a set of observations as mixtures of pure (extreme) patterns. If the patterns are actual observations of the sample, we refer to them as archetypoids. For the first time, we propose to use archetypoid analysis for binary observations. This tool can contribute to the understanding of a binary data set, as in the multivariate case. We illustrate the advantages of the proposed methodology in a simulation study and two applications, one exploring objects (rows) and the other exploring items (columns). One is related to determining student skill set profiles and the other to describing item response functions.

Federated learning refers to a distributed learning scenario in which users/nodes keep their data private but only share intermediate locally computed iterates with the master node. The master, in turn, shares a global aggregate of these iterates with all the nodes at each iteration. In this work, we consider a wireless federated learning scenario where the nodes communicate to and from the master node via a wireless channel. Current and upcoming technologies such as 5G (and beyond) will operate mostly in a non-orthogonal multiple access (NOMA) mode where transmissions from the users occupy the same bandwidth and interfere at the access point. These technologies naturally lend themselves to an "over-the-air" superposition whereby information received from the user nodes can be directly summed at the master node. However, over-the-air aggregation also means that the channel noise can corrupt the algorithm iterates at the time of aggregation at the master. This iteration noise introduces a novel set of challenges that have not been previously studied in the literature. It needs to be treated differently from the well-studied setting of noise or corruption in the dataset itself. In this work, we first study the subspace learning problem in a federated over-the-air setting. Subspace learning involves computing the subspace spanned by the top $r$ singular vectors of a given matrix. We develop a federated over-the-air version of the power method (FedPM) and show that its iterates converge as long as (i) the channel noise is very small compared to the $r$-th singular value of the matrix; and (ii) the ratio between its $(r+1)$-th and $r$-th singular value is smaller than a constant less than one. The second important contribution of this work is to show how over-the-air FedPM can be used to obtain a provably accurate federated solution for subspace tracking in the presence of missing data.

We propose a method for estimation in high-dimensional linear models with nominal categorical data. Our estimator, called SCOPE, fuses levels together by making their corresponding coefficients exactly equal. This is achieved using the minimax concave penalty on differences between the order statistics of the coefficients for a categorical variable, thereby clustering the coefficients. We provide an algorithm for exact and efficient computation of the global minimum of the resulting nonconvex objective in the case with a single variable with potentially many levels, and use this within a block coordinate descent procedure in the multivariate case. We show that an oracle least squares solution that exploits the unknown level fusions is a limit point of the coordinate descent with high probability, provided the true levels have a certain minimum separation; these conditions are known to be minimal in the univariate case. We demonstrate the favourable performance of SCOPE across a range of real and simulated datasets. An R package CatReg implementing SCOPE for linear models and also a version for logistic regression is available on CRAN.

Compressing deep neural network (DNN) models becomes a very important and necessary technique for real-world applications, such as deploying those models on mobile devices. Knowledge distillation is one of the most popular methods for model compression, and many studies have been made on developing this technique. However, those studies mainly focused on classification problems, and very few attempts have been made on regression problems, although there are many application of DNNs on regression problems. In this paper, we propose a new formalism of knowledge distillation for regression problems. First, we propose a new loss function, teacher outlier rejection loss, which rejects outliers in training samples using teacher model predictions. Second, we consider a multi-task network with two outputs: one estimates training labels which is in general contaminated by noisy labels; And the other estimates teacher model's output which is expected to modify the noise labels following the memorization effects. By considering the multi-task network, training of the feature extraction of student models becomes more effective, and it allows us to obtain a better student model than one trained from scratch. We performed comprehensive evaluation with one simple toy model: sinusoidal function, and two open datasets: MPIIGaze, and Multi-PIE. Our results show consistent improvement in accuracy regardless of the annotation error level in the datasets.

Knowledge Graphs (KGs) are graph-structured knowledge bases storing factual information about real-world entities. Understanding the uniqueness of each entity is crucial to the analyzing, sharing, and reusing of KGs. Traditional profiling technologies encompass a vast array of methods to find distinctive features in various applications, which can help to differentiate entities in the process of human understanding of KGs. In this work, we present a novel profiling approach to identify distinctive entity features. The distinctiveness of features is carefully measured by a HAS model, which is a scalable representation learning model to produce a multi-pattern entity embedding. We fully evaluate the quality of entity profiles generated from real KGs. The results show that our approach facilitates human understanding of entities in KGs.

The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in the area of artificial intelligence to applications in education). Apart from the usual measures of efficiency (e.g. CPU time), the possibility of visual and/or readable proofs is also an expected output against which the geometry automated theorem provers (GATP) should be measured. The implementation of a competition between GATP would allow to create a test bench for GATP developers to improve the existing ones and to propose new ones. It would also allow to establish a ranking for GATP that could be used by "clients" (e.g. developers of educational e-learning systems) to choose the best implementation for a given intended use.

When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing, beforehand, the possible ways to solve a problem. Hence the need for an automated theorem prover that provide proofs as they would be written by a student. To achieve this objective, logic programming is a natural tool due to the similarity of its reasoning with a mathematical proof by inference. In this paper, we present the core ideas we used to implement such a prover, from its encoding in Prolog to the generation of the complete set of proofs. However, when dealing with educational aspects, there are many challenges to overcome. We also present the main issues we encountered, as well as the chosen solutions. The QED-Tutrix software [15, 19] provides an environment where a highschool student can solve geometry proof problems. One of its key features is that it allows the student to provide proof elements in any order, not limiting them to forward-or backward-chaining. For instance, when solving the simple problem "prove that a quadrilateral with three right angles is a rectangle", the student can provide any element of any possible proof, such as a direct consequence of the hypotheses ("if two lines are perpendicular to a third, they are parallel"), a necessary premise for the conclusion ("a rectangle is a quadrilateral that has four right angles"), or anything in between ("the quadrilateral ABCD is a parallelogram"). A second key feature is the tutoring aspect. When the student is stuck is the resolution, the software is able to provide them with relevant messages. In the previous example, if the student entered "the quadrilateral ABCD is a parallelogram" and is stuck afterwards, the software identifies that they are working on a proof using parallelogram properties, and will provide them messages such as "what is the definition of a parallelogram?" or "is there a relation between parallelogram and rectangle?" These features, the flexibility in exploration and the tutoring, are very interesting from a mathematics education perspective, but come with a cost.

The AI-Base Module will be implemented across 5,000 Atal Tinkering Labs (ATL), empowering 2.5 million students. The module is likely to be introduced to ATL students on 27 February. The module contains activities, videos and experiments that enable students to work through and learn the various concepts of AI. Niti Aayog CEO Amitabh Kant said the AI module was critical since it was targeted at young children. "This is path breaking, it combines playing and academics and our job is to make things very interesting. We want to make artificial intelligence a great fun, so that children can enjoy it, they can evolve and learn and take India forward," said Kant. "This is the first ever industry government academia initiative on such a scale to keep the school students abreast of latest technologies," said Mission Director Atal Innovation Mission, NITI Aayog R Ramanan.

The third section of the curriculum is all about practice. In order to truly master the concepts above you will need to use the skills in some projects that ideally closely resemble a real-world application. By doing this you will encounter problems to work through such as missing and erroneous data and develop a deep level of expertise in the subject. In this last section, I will list some good places you can get this practical experience from for free. "With deliberate practice, however, the goal is not just to reach your potential but to build it, to make things possible that were not possible before. This requires challenging homeostasis -- getting out of your comfort zone -- and forcing your brain or your body to adapt.",

Artificial intelligence is an immensely powerful tool, the effects of which are being felt across a range of industries, sectors, and disciplines. Its application to challenges ranging from wildlife preservation to deep space exploration proves its versatility, while machine learning courses are being taught to the next generation of researchers so that its full potential can be realized in years to come. Of course, even education itself is being shaped by the influence of AI, so here is a look at how machine learning is having an impact on human learning. One of the biggest struggles that teachers face today is being able to effectively manage their time and balance the administrative responsibilities that are unavoidable as part of their roles while also being able to dedicate themselves to the job of actually engaging with students. AI offers up the power to automate many of the more mundane tasks involved in the job of teaching, empowering educators to focus on the things that got them interested in imparting knowledge to others in the first place.