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We consider the problem of training a classification model with group annotated training data. Recent work has established that, if there is distribution shift across different groups, models trained using the standard empirical risk minimization (ERM) objective suffer from poor performance on minority groups and that group distributionally robust optimization (Group-DRO) objective is a better alternative. The starting point of this paper is the observation that though Group-DRO performs better than ERM on minority groups for some benchmark datasets, there are several other datasets where it performs much worse than ERM. Inspired by ideas from the closely related problem of domain generalization, this paper proposes a new and simple algorithm that explicitly encourages learning of features that are shared across various groups. The key insight behind our proposed algorithm is that while Group-DRO focuses on groups with worst regularized loss, focusing instead, on groups that enable better performance even on other groups, could lead to learning of shared/common features, thereby enhancing minority performance beyond what is achieved by Group-DRO. Empirically, we show that our proposed algorithm matches or achieves better performance compared to strong contemporary baselines including ERM and Group-DRO on standard benchmarks on both minority groups and across all groups. Theoretically, we show that the proposed algorithm is a descent method and finds first order stationary points of smooth nonconvex functions.

In a sports competition, a team might lose a powerful incentive to exert full effort if its final rank does not depend on the outcome of the matches still to be played. Therefore, the organiser should reduce the probability of such a situation to the extent possible. Our paper provides a classification scheme to identify these weakly (where one team is indifferent) or strongly (where both teams are indifferent) stakeless games. A statistical model is estimated to simulate the UEFA Champions League groups and compare the candidate schedules used in the 2021/22 season according to the competitiveness of the matches played in the last round(s). The option followed in four of the eight groups is found to be optimal under a wide set of parameters. Minimising the number of strongly stakeless matches is verified to be a likely goal in the computer draw of the fixture that remains hidden from the public.

Recruitment in large organisations often involves interviewing a large number of candidates. The process is resource intensive and complex. Therefore, it is important to carry it out efficiently and effectively. Planning the selection process consists of several problems, each of which maps to one or the other well-known computing problem. Research that looks at each of these problems in isolation is rich and mature. However, research that takes an integrated view of the problem is not common. In this paper, we take two of the most important aspects of the application processing problem, namely review/interview panel creation and interview scheduling. We have implemented our approach as a prototype system and have used it to automatically plan the interview process of a real-life data set. Our system provides a distinctly better plan than the existing practice, which is predominantly manual. We have explored various algorithmic options and have customised them to solve these panel creation and interview scheduling problems. We have evaluated these design options experimentally on a real data set and have presented our observations. Our prototype and experimental process and results may be a very good starting point for a full-fledged development project for automating application processing process.

We study the problem of testing whether a function $f: \mathbb{R}^n \to \mathbb{R}$ is a polynomial of degree at most $d$ in the \emph{distribution-free} testing model. Here, the distance between functions is measured with respect to an unknown distribution $\mathcal{D}$ over $\mathbb{R}^n$ from which we can draw samples. In contrast to previous work, we do not assume that $\mathcal{D}$ has finite support. We design a tester that given query access to $f$, and sample access to $\mathcal{D}$, makes $(d/\varepsilon)^{O(1)}$ many queries to $f$, accepts with probability $1$ if $f$ is a polynomial of degree $d$, and rejects with probability at least $2/3$ if every degree-$d$ polynomial $P$ disagrees with $f$ on a set of mass at least $\varepsilon$ with respect to $\mathcal{D}$. Our result also holds under mild assumptions when we receive only a polynomial number of bits of precision for each query to $f$, or when $f$ can only be queried on rational points representable using a logarithmic number of bits. Along the way, we prove a new stability theorem for multivariate polynomials that may be of independent interest.

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.

This paper studies the application of reconfigurable intelligent surface (RIS) to cooperative non-orthogonal multiple access (C-NOMA) networks with simultaneous wireless information and power transfer (SWIPT). We aim for maximizing the rate of the strong user with guaranteed weak user's quality of service (QoS) by jointly optimizing power splitting factors, beamforming coefficients, and RIS reflection coefficients in two transmission phases. The formulated problem is difficult to solve due to its complex and non-convex constraints. To tackle this challenging problem, we first use alternating optimization (AO) framework to transform it into three subproblems, and then use the penalty-based arithmetic-geometric mean approximation (PBAGM) algorithm and the successive convex approximation (SCA)-based method to solve them. Numerical results verify the superiority of the proposed algorithm over the baseline schemes.

This paper describes a hand geometry biometric identification system. We have acquired a database of 22 people, 10 acquisitions per person, using a conventional document scanner. We propose a feature extraction and classifier. The experimental results reveal a maximum identification rate equal to 93.64%, and a minimum value of the detection cost function equal to 2.92% using a multi layer perceptron classifier.

Given a matrix $A$ and vector $b$ with polynomial entries in $d$ real variables $\delta=(\delta_1,\ldots,\delta_d)$ we consider the following notion of feasibility: the pair $(A,b)$ is locally feasible if there exists an open neighborhood $U$ of $0$ such that for every $\delta\in U$ there exists $x$ satisfying $A(\delta)x\ge b(\delta)$ entry-wise. For $d=1$ we construct a polynomial time algorithm for deciding local feasibility. For $d \ge 2$ we show local feasibility is NP-hard. As an application (which was the primary motivation for this work) we give a computer-assisted proof of ergodicity of the following elementary 1D cellular automaton: given the current state $\eta_t \in \{0,1\}^{\mathbb{Z}}$ the next state $\eta_{t+1}(n)$ at each vertex $n\in \mathbb{Z}$ is obtained by $\eta_{t+1}(n)= \text{NAND}\big(\text{BSC}_\delta(\eta_t(n-1)), \text{BSC}_\delta(\eta_t(n))\big)$. Here the binary symmetric channel $\text{BSC}_\delta$ takes a bit as input and flips it with probability $\delta$ (and leaves it unchanged with probability $1-\delta$). We also consider the problem of broadcasting information on the 2D-grid of noisy binary-symmetric channels $\text{BSC}_\delta$, where each node may apply an arbitrary processing function to its input bits. We prove that there exists $\delta_0'>0$ such that for all noise levels $0<\delta<\delta_0'$ it is impossible to broadcast information for any processing function, as conjectured in Makur, Mossel, Polyanskiy (ISIT 2021).

A palindromic substring $T[i.. j]$ of a string $T$ is said to be a shortest unique palindromic substring (SUPS) in $T$ for an interval $[p, q]$ if $T[i.. j]$ is a shortest one such that $T[i.. j]$ occurs only once in $T$, and $[i, j]$ contains $[p, q]$. The SUPS problem is, given a string $T$ of length $n$, to construct a data structure that can compute all the SUPSs for any given query interval. It is known that any SUPS query can be answered in $O(\alpha)$ time after $O(n)$-time preprocessing, where $\alpha$ is the number of SUPSs to output [Inoue et al., 2018]. In this paper, we first show that $\alpha$ is at most $4$, and the upper bound is tight. Also, we present an algorithm to solve the SUPS problem for a sliding window that can answer any query in $O(\log\log W)$ time and update data structures in amortized $O(\log\sigma)$ time, where $W$ is the size of the window, and $\sigma$ is the alphabet size. Furthermore, we consider the SUPS problem in the after-edit model and present an efficient algorithm. Namely, we present an algorithm that uses $O(n)$ time for preprocessing and answers any $k$ SUPS queries in $O(\log n\log\log n + k\log\log n)$ time after single character substitution. As a by-product, we propose a fully-dynamic data structure for range minimum queries (RmQs) with a constraint where the width of each query range is limited to polylogarithmic. The constrained RmQ data structure can answer such a query in constant time and support a single-element edit operation in amortized constant time.

The success of deep learning attracted interest in whether the brain learns hierarchical representations using gradient-based learning. However, current biologically plausible methods for gradient-based credit assignment in deep neural networks need infinitesimally small feedback signals, which is problematic in biologically realistic noisy environments and at odds with experimental evidence in neuroscience showing that top-down feedback can significantly influence neural activity. Building upon deep feedback control (DFC), a recently proposed credit assignment method, we combine strong feedback influences on neural activity with gradient-based learning and show that this naturally leads to a novel view on neural network optimization. Instead of gradually changing the network weights towards configurations with low output loss, weight updates gradually minimize the amount of feedback required from a controller that drives the network to the supervised output label. Moreover, we show that the use of strong feedback in DFC allows learning forward and feedback connections simultaneously, using a learning rule fully local in space and time. We complement our theoretical results with experiments on standard computer-vision benchmarks, showing competitive performance to backpropagation as well as robustness to noise. Overall, our work presents a fundamentally novel view of learning as control minimization, while sidestepping biologically unrealistic assumptions.