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In this perspective paper we study the effect of non independent and identically distributed (non-IID) data on federated online learning to rank (FOLTR) and chart directions for future work in this new and largely unexplored research area of Information Retrieval. In the FOLTR process, clients join a federation to jointly create an effective ranker from the implicit click signal originating in each client, without the need to share data (documents, queries, clicks). A well-known factor that affects the performance of federated learning systems, and that poses serious challenges to these approaches, is the fact that there may be some type of bias in the way the data is distributed across clients. While FOLTR systems are on their own rights a type of federated learning system, the presence and effect of non-IID data in FOLTR has not been studied. To this aim, we first enumerate possible data distribution settings that may showcase data bias across clients and thus give rise to the non-IID problem. Then, we study the impact of each of these settings on the performance of the current state-of-the-art FOLTR approach, the Federated Pairwise Differentiable Gradient Descent (FPDGD), and we highlight which data distributions may pose a problem for FOLTR methods. We also explore how common approaches proposed in the federated learning literature address non-IID issues in FOLTR. This allows us to unveil new research gaps that, we argue, future research in FOLTR should consider. This is an important contribution to the current state of the field of FOLTR because, for FOLTR systems to be deployed, the factors affecting their performance, including the impact of non-IID data, need to thoroughly be understood.

Optimal feedback control (OFC) is a theory from the motor control literature that explains how humans move their body to achieve a certain goal, e.g., pointing with the finger. OFC is based on the assumption that humans aim to control their body optimally, within the constraints imposed by body, environment, and task. In this paper, we explain how this theory can be applied to understanding Human-Computer Interaction (HCI) in the case of pointing. We propose that the human body and computer dynamics can be interpreted as a single dynamical system. The system state is controlled by the user via muscle control signals, and estimated from observations. Between-trial variability arises from signal-dependent control noise and observation noise. We compare four different models from optimal control theory and evaluate to what degree these models can replicate movements in the case of mouse pointing. We introduce a procedure to identify parameters that best explain observed user behavior. To support HCI researchers in simulating, analyzing, and optimizing interaction movements, we provide the Python toolbox OFC4HCI. We conclude that OFC presents a powerful framework for HCI to understand and simulate motion of the human body and of the interface on a moment by moment basis.

The number of down-steps between pairs of up-steps in $k_t$-Dyck paths, a generalization of Dyck paths consisting of steps $\{(1, k), (1, -1)\}$ such that the path stays (weakly) above the line $y=-t$, is studied. Results are proved bijectively and by means of generating functions, and lead to several interesting identities as well as links to other combinatorial structures. In particular, there is a connection between $k_t$-Dyck paths and perforation patterns for punctured convolutional codes (binary matrices) used in coding theory. Surprisingly, upon restriction to usual Dyck paths this yields a new combinatorial interpretation of Catalan numbers.

Many existing algorithms for streaming geometric data analysis have been plagued by exponential dependencies in the space complexity, which are undesirable for processing high-dimensional data sets. In particular, once $d\geq\log n$, there are no known non-trivial streaming algorithms for problems such as maintaining convex hulls and L\"owner-John ellipsoids of $n$ points, despite a long line of work in streaming computational geometry since [AHV04]. We simultaneously improve these results to $\mathrm{poly}(d,\log n)$ bits of space by trading off with a $\mathrm{poly}(d,\log n)$ factor distortion. We achieve these results in a unified manner, by designing the first streaming algorithm for maintaining a coreset for $\ell_\infty$ subspace embeddings with $\mathrm{poly}(d,\log n)$ space and $\mathrm{poly}(d,\log n)$ distortion. Our algorithm also gives similar guarantees in the \emph{online coreset} model. Along the way, we sharpen results for online numerical linear algebra by replacing a log condition number dependence with a $\log n$ dependence, answering a question of [BDM+20]. Our techniques provide a novel connection between leverage scores, a fundamental object in numerical linear algebra, and computational geometry. For $\ell_p$ subspace embeddings, we give nearly optimal trade-offs between space and distortion for one-pass streaming algorithms. For instance, we give a deterministic coreset using $O(d^2\log n)$ space and $O((d\log n)^{1/2-1/p})$ distortion for $p>2$, whereas previous deterministic algorithms incurred a $\mathrm{poly}(n)$ factor in the space or the distortion [CDW18]. Our techniques have implications in the offline setting, where we give optimal trade-offs between the space complexity and distortion of subspace sketch data structures. To do this, we give an elementary proof of a "change of density" theorem of [LT80] and make it algorithmic.

In this paper we propose a methodology to accelerate the resolution of the so-called "Sorted L-One Penalized Estimation" (SLOPE) problem. Our method leverages the concept of "safe screening", well-studied in the literature for \textit{group-separable} sparsity-inducing norms, and aims at identifying the zeros in the solution of SLOPE. More specifically, we derive a set of \(\tfrac{n(n+1)}{2}\) inequalities for each element of the \(n\)-dimensional primal vector and prove that the latter can be safely screened if some subsets of these inequalities are verified. We propose moreover an efficient algorithm to jointly apply the proposed procedure to all the primal variables. Our procedure has a complexity \(\mathcal{O}(n\log n + LT)\) where \(T\leq n\) is a problem-dependent constant and \(L\) is the number of zeros identified by the tests. Numerical experiments confirm that, for a prescribed computational budget, the proposed methodology leads to significant improvements of the solving precision.

We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system+bath) is held in canonical thermal equilibrium by weak coupling with a "super-bath". Our approach is a generalization of now standard typicality algorithms for computing the quantum expectation value of observables of bare quantum systems via trace estimators and Krylov subspace methods. In particular, our algorithm makes use of the fact that the reduced system density, when the bath is measured in a given random state, tends to concentrate about the corresponding thermodynamic averaged reduced system density. Theoretical error analysis and numerical experiments are given to validate the accuracy of our algorithm. Further numerical experiments demonstrate the potential of our approach for applications including the study of quantum phase transitions and entanglement entropy for long-range interaction systems.

With the advent of open source software, a veritable treasure trove of previously proprietary software development data was made available. This opened the field of empirical software engineering research to anyone in academia. Data that is mined from software projects, however, requires extensive processing and needs to be handled with utmost care to ensure valid conclusions. Since the software development practices and tools have changed over two decades, we aim to understand the state-of-the-art research workflows and to highlight potential challenges. We employ a systematic literature review by sampling over one thousand papers from leading conferences and by analyzing the 286 most relevant papers from the perspective of data workflows, methodologies, reproducibility, and tools. We found that an important part of the research workflow involving dataset selection was particularly problematic, which raises questions about the generality of the results in existing literature. Furthermore, we found a considerable number of papers provide little or no reproducibility instructions -- a substantial deficiency for a data-intensive field. In fact, 33% of papers provide no information on how their data was retrieved. Based on these findings, we propose ways to address these shortcomings via existing tools and also provide recommendations to improve research workflows and the reproducibility of research.

Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by extending a minimal modal base logic of static functional dependencies. We define a logic for dynamical systems with single time steps, provide a complete axiomatic proof calculus, and show the decidability of the satisfiability problem for a substantial fragment. The system comes in two guises: modal and first-order, that naturally complement each other. Next, we consider a timed semantics for our logic, as an intermediate between state spaces and temporal universes for the unfoldings of a dynamical system. We prove completeness and decidability by combining techniques from dynamic-epistemic logic and modal logic of functional dependencies with complex terms for objects. Also, we extend these results to the timed logic with functional symbols and term identity. Finally, we conclude with a brief outlook on how the system proposed here connects with richer temporal logics of system behavior, and with dynamic topological logic.

Structural data well exists in Web applications, such as social networks in social media, citation networks in academic websites, and threads data in online forums. Due to the complex topology, it is difficult to process and make use of the rich information within such data. Graph Neural Networks (GNNs) have shown great advantages on learning representations for structural data. However, the non-transparency of the deep learning models makes it non-trivial to explain and interpret the predictions made by GNNs. Meanwhile, it is also a big challenge to evaluate the GNN explanations, since in many cases, the ground-truth explanations are unavailable. In this paper, we take insights of Counterfactual and Factual (CF^2) reasoning from causal inference theory, to solve both the learning and evaluation problems in explainable GNNs. For generating explanations, we propose a model-agnostic framework by formulating an optimization problem based on both of the two casual perspectives. This distinguishes CF^2 from previous explainable GNNs that only consider one of them. Another contribution of the work is the evaluation of GNN explanations. For quantitatively evaluating the generated explanations without the requirement of ground-truth, we design metrics based on Counterfactual and Factual reasoning to evaluate the necessity and sufficiency of the explanations. Experiments show that no matter ground-truth explanations are available or not, CF^2 generates better explanations than previous state-of-the-art methods on real-world datasets. Moreover, the statistic analysis justifies the correlation between the performance on ground-truth evaluation and our proposed metrics.

In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.