The Young Physicists Tournament is an established team-oriented scientific competition between high school students from 37 countries on 5 continents. The competition consists of scientific discussions called Fights. Three or four teams participate in each Fight, each of whom presents a problem while rotating the roles of Presenter, Opponent, Reviewer, and Observer among them. The rules of a few countries require that each team announce in advance 3 problems they will present at the national tournament. The task of the organizers is to choose the composition of Fights in such a way that each team presents each of its chosen problems exactly once and within a single Fight no problem is presented more than once. Besides formalizing these feasibility conditions, in this paper we formulate several additional fairness conditions for tournament schedules. We show that the fulfillment of some of them can be ensured by constructing suitable edge colorings in bipartite graphs. To find fair schedules, we propose integer linear programs and test them on real as well as randomly generated data.

Inertial measurement units are commonly used to estimate the attitude of moving objects. Numerous nonlinear filter approaches have been proposed for solving the inherent sensor fusion problem. However, when a large range of different dynamic and static rotational and translational motions is considered, the attainable accuracy is limited by the need for situation-dependent adjustment of accelerometer and gyroscope fusion weights. We investigate to what extent these limitations can be overcome by means of artificial neural networks and how much domain-specific optimization of the neural network model is required to outperform the conventional filter solution. A diverse set of motion recordings with a marker-based optical ground truth is used for performance evaluation and comparison. The proposed neural networks are found to outperform the conventional filter across all motions only if domain-specific optimizations are introduced. We conclude that they are a promising tool for inertial-sensor-based real-time attitude estimation, but both expert knowledge and rich datasets are required to achieve top performance.

In value-based reinforcement learning (RL), unlike in supervised learning, the agent faces not a single, stationary, approximation problem, but a sequence of value prediction problems. Each time the policy improves, the nature of the problem changes, shifting both the distribution of states and their values. In this paper we take a novel perspective, arguing that the value prediction problems faced by an RL agent should not be addressed in isolation, but rather as a single, holistic, prediction problem. An RL algorithm generates a sequence of policies that, at least approximately, improve towards the optimal policy. We explicitly characterize the associated sequence of value functions and call it the value-improvement path. Our main idea is to approximate the value-improvement path holistically, rather than to solely track the value function of the current policy. Specifically, we discuss the impact that this holistic view of RL has on representation learning. We demonstrate that a representation that spans the past value-improvement path will also provide an accurate value approximation for future policy improvements. We use this insight to better understand existing approaches to auxiliary tasks and to propose new ones. To test our hypothesis empirically, we augmented a standard deep RL agent with an auxiliary task of learning the value-improvement path. In a study of Atari 2600 games, the augmented agent achieved approximately double the mean and median performance of the baseline agent.

As neural networks grow larger and more complex and data-hungry, training costs are skyrocketing. Especially when lifelong learning is necessary, such as in recommender systems or self-driving cars, this might soon become unsustainable. In this study, we present the first optical co-processor able to accelerate the training phase of digitally-implemented neural networks. We rely on direct feedback alignment as an alternative to backpropagation, and perform the error projection step optically. Leveraging the optical random projections delivered by our co-processor, we demonstrate its use to train a neural network for handwritten digits recognition.

The molecular dipole moment ($\boldsymbol{\mu}$) is a central quantity in chemistry. It is essential in predicting infrared and sum-frequency generation spectra, as well as induction and long-range electrostatic interactions. Furthermore, it can be extracted directly from high-level quantum mechanical calculations, making it an ideal target for machine learning (ML). In this work, we choose to represent this quantity with a physically inspired ML model that captures two distinct physical effects: local atomic polarization is captured within the symmetry-adapted Gaussian process regression (SA-GPR) framework, which assigns a (vector) dipole moment to each atom, while movement of charge across the entire molecule is captured by assigning a partial (scalar) charge to each atom. The resulting "MuML" models are fitted together to reproduce molecular $\boldsymbol{\mu}$ computed using high-level coupled-cluster theory (CCSD) and density functional theory (DFT) on the QM7b dataset. The combined model shows excellent transferability when applied to a showcase dataset of larger and more complex molecules, approaching the accuracy of DFT at a small fraction of the computational cost. We also demonstrate that the uncertainty in the predictions can be estimated reliably using a calibrated committee model. The ultimate performance of the models depends, however, on the details of the system at hand, with the scalar model being clearly superior when describing large molecules whose dipole is almost entirely generated by charge separation. These observations point to the importance of simultaneously accounting for the local and non-local effects that contribute to $\boldsymbol{\mu}$; further, they define a challenging task to benchmark future models, particularly those aimed at the description of condensed phases.

It can be seen The differential geometric approach to probability theory as a natural choice of metric as it is the only Riemannian and statistics has met increasing interest in the past metric that is invariant with respect to transformation by years, from the theoretical point of view as well as in a sufficient statistic, or a diffeomorphic transformation of applications. In this approach, probability distributions the support in the nonparametric case (Cencov, 2000; are seen as elements of a differentiable manifold, on which Bauer et al., 2016). Arguably the most famous example a metric structure is defined through the choice of a of Fisher information geometry of a statistical model is Riemannian metric. Two very important ones are the that of the univariate Gaussian model, which is hyperbolic. Wasserstein metric, central in optimal transport, and The geometries of other parametric families such as the Fisher information metric (also called Fisher-Rao the multivariate Gaussian model (Atkinson and Mitchell, metric), essential in information geometry. Unlike optimal 1981; Skovgaard, 1984), the family of gamma distributions transport, information geometry is foremost concerned (Arwini and Dodson, 2008; Rebbah et al., 2019), or more with parametric families of probability distributions, and generally location-scale models (Said et al., 2019), among defines a Riemannian structure on the parameter space others, have also received a lot of attention.

Most existing black-box optimization methods assume that all variables in the system being optimized have equal cost and can change freely at each iteration. However, in many real world systems, inputs are passed through a sequence of different operations or modules, making variables in earlier stages of processing more costly to update. Such structure imposes a cost on switching variables in early parts of a data processing pipeline. In this work, we propose a new algorithm for switch cost-aware optimization called Lazy Modular Bayesian Optimization (LaMBO). This method efficiently identifies the global optimum while minimizing cost through a passive change of variables in early modules. The method is theoretical grounded and achieves vanishing regret when augmented with switching cost. We apply LaMBO to multiple synthetic functions and a three-stage image segmentation pipeline used in a neuroscience application, where we obtain promising improvements over prevailing cost-aware Bayesian optimization algorithms. Our results demonstrate that LaMBO is an effective strategy for black-box optimization that is capable of minimizing switching costs in modular systems.

In this article, we consider the problem of high-dimensional conditional independence testing, which is a key building block in statistics and machine learning. We propose a double generative adversarial networks (GANs)-based inference procedure. We first introduce a double GANs framework to learn two generators, and integrate the two generators to construct a doubly-robust test statistic. We next consider multiple generalized covariance measures, and take their maximum as our test statistic. Finally, we obtain the empirical distribution of our test statistic through multiplier bootstrap. We show that our test controls type-I error, while the power approaches one asymptotically. More importantly, these theoretical guarantees are obtained under much weaker and practically more feasible conditions compared to existing tests. We demonstrate the efficacy of our test through both synthetic and real datasets.

We study the convergence rates of the EM algorithm for learning two-component mixed linear regression under all regimes of signal-to-noise ratio (SNR). We resolve a long-standing question that many recent results have attempted to tackle: we completely characterize the convergence behavior of EM, and show that the EM algorithm achieves minimax optimal sample complexity under all SNR regimes. In particular, when the SNR is sufficiently large, the EM updates converge to the true parameter $\theta^{*}$ at the standard parametric convergence rate $\mathcal{O}((d/n)^{1/2})$ after $\mathcal{O}(\log(n/d))$ iterations. In the regime where the SNR is above $\mathcal{O}((d/n)^{1/4})$ and below some constant, the EM iterates converge to a $\mathcal{O}({\rm SNR}^{-1} (d/n)^{1/2})$ neighborhood of the true parameter, when the number of iterations is of the order $\mathcal{O}({\rm SNR}^{-2} \log(n/d))$. In the low SNR regime where the SNR is below $\mathcal{O}((d/n)^{1/4})$, we show that EM converges to a $\mathcal{O}((d/n)^{1/4})$ neighborhood of the true parameters, after $\mathcal{O}((n/d)^{1/2})$ iterations. Notably, these results are achieved under mild conditions of either random initialization or an efficiently computable local initialization. By providing tight convergence guarantees of the EM algorithm in middle-to-low SNR regimes, we fill the remaining gap in the literature, and significantly, reveal that in low SNR, EM changes rate, matching the $n^{-1/4}$ rate of the MLE, a behavior that previous work had been unable to show.

Graphs neural networks (GNNs) learn node features by aggregating and combining neighbor information, which have achieved promising performance on many graph tasks. However, GNNs are mostly treated as black-boxes and lack human intelligible explanations. Thus, they cannot be fully trusted and used in certain application domains if GNN models cannot be explained. In this work, we propose a novel approach, known as XGNN, to interpret GNNs at the model-level. Our approach can provide high-level insights and generic understanding of how GNNs work. In particular, we propose to explain GNNs by training a graph generator so that the generated graph patterns maximize a certain prediction of the model.We formulate the graph generation as a reinforcement learning task, where for each step, the graph generator predicts how to add an edge into the current graph. The graph generator is trained via a policy gradient method based on information from the trained GNNs. In addition, we incorporate several graph rules to encourage the generated graphs to be valid. Experimental results on both synthetic and real-world datasets show that our proposed methods help understand and verify the trained GNNs. Furthermore, our experimental results indicate that the generated graphs can provide guidance on how to improve the trained GNNs.