Ensemble methods have been widely used for improving the results of the best single classification model. Indeed, a large body of works have achieved better results mainly by applying one specific ensemble method. However, very few works analyze complex fusion schemes using heterogeneous ensemble strategies. This paper is three-fold: 1) It provides a tutorial of the most popular ensemble methods, 2) analyzes the best ensembles using MNIST as guiding thread and 3) shows that complex fusion architectures based on heterogeneous ensembles can be considered as a mode of taking benefit from diversity. We introduce a complex fusion design that achieves a new record in MNIST with only 10 misclassified images.

Analysing Affective Behavior in the First ABA W 2020 Competition Dimitrios Kollias 1, Attila Schulc 2, Elnar Hajiyev 2 and Stefanos Zafeiriou 1 1 Department of Computing, Imperial College London, UK 2 Realeyes - Emotional Intelligence Abstract -- The Affective Behavior Analysis in-the- wild (ABA W) 2020 Competition is the first Competition aiming at automatic analysis of the three main behavior tasks of valence-arousal estimation, basic expression recognition and action unit detection. It is split into three Challenges, each one addressing a respective behavior task. For the Challenges, we provide a common benchmark database, Aff-Wild2, which is a large scale in-the-wild database and the first one annotated for all these three tasks. In this paper, we describe this Competition, to be held in conjunction with the IEEE Conference on Face and Gesture Recognition, May 2020, in Buenos Aires, Argentina. We present the three Challenges, with the utilized Competition corpora. We outline the evaluation metrics and present the baseline methodologies and the obtained results when these are applied to each Challenge.

We provide a novel approach and an exploratory study for modelling life event choices and occurrence from a probabilistic perspective through causal discovery and survival analysis. Our approach is formulated as a bi-level problem. In the upper level, we build the life events graph, using causal discovery tools. In the lower level, for the pairs of life events, time-to-event modelling through survival analysis is applied to model time-dependent transition probabilities. Several life events were analysed, such as getting married, buying a new car, child birth, home relocation and divorce, together with the socio-demographic attributes for survival modelling, some of which are age, nationality, number of children, number of cars and home ownership. The data originates from a survey conducted in Dortmund, Germany, with the questionnaire containing a series of retrospective questions about residential and employment biography, travel behaviour and holiday trips, as well as socio-economic characteristic. Although survival analysis has been used in the past to analyse life-course data, this is the first time that a bi-level model has been formulated. The inclusion of a causal discovery algorithm in the upper-level allows us to first identify causal relationships between life-course events and then understand the factors that might influence transition rates between events. This is very different from more classic choice models where causal relationships are subject to expert interpretations based on model results.

Real-time Linear Operator Construction and State Estimation with Kalman Filter Tsuyoshi Ishizone 1 Graduate School of Advanced Mathematical Sciences, Meiji University and Kazuyuki Nakamura Department of Interdisciplinary Mathematical Sciences, Meiji University JST, PRESTO Abstract Kalman filter is the most powerful tool for estimation of the states of the linear Gaussian system. In addition, used this method, expectation maximization algorithm can estimate the parameters of the model. Thus, we propose new method that can estimate the transition matrices and the states of the system in real-time. Applied to damped oscillation model, we have obtained extraordinary performance to estimate the matrices. Also, introduced localization and spatially uniformity to the method, we have demonstrated that our methods could reduce noise in high-dimensional spatiotemporal data. Moreover, this methodology has potential in areas such as weather forecast and vector field analysis. Keywords: state space model, noise reduction, flow analysis, online learning, weather forecast 1 INTRODUCTION A quick tool of noise reduction and short-term prediction is important for areas such as weather forecast and adjusting scanning probe microscope (SPM). In weather forecast, engineers need a speedy denoising method to utilize the result for instantaneous forecast.

Media is generally stored digitally and is therefore discrete. Many successful deep distribution models in deep learning learn a density, i.e., the distribution of a continuous random variable. Na\"ive optimization on discrete data leads to arbitrarily high likelihoods, and instead, it has become standard practice to add noise to datapoints. In this paper, we present a general framework for dequantization that captures existing methods as a special case. We derive two new dequantization objectives: importance-weighted (iw) dequantization and R\'enyi dequantization. In addition, we introduce autoregressive dequantization (ARD) for more flexible dequantization distributions. Empirically we find that iw and R\'enyi dequantization considerably improve performance for uniform dequantization distributions. ARD achieves a negative log-likelihood of 3.06 bits per dimension on CIFAR10, which to the best of our knowledge is state-of-the-art among distribution models that do not require autoregressive inverses for sampling.

Academic research in the field of autonomous vehicles has reached high popularity in recent years related to several topics as sensor technologies, V2X communications, safety, security, decision making, control, and even legal and standardization rules. Besides classic control design approaches, Artificial Intelligence and Machine Learning methods are present in almost all of these fields. Another part of research focuses on different layers of Motion Planning, such as strategic decisions, trajectory planning, and control. A wide range of techniques in Machine Learning itself have been developed, and this article describes one of these fields, Deep Reinforcement Learning (DRL). The paper provides insight into the hierarchical motion planning problem and describes the basics of DRL. The main elements of designing such a system are the modeling of the environment, the modeling abstractions, the description of the state and the perception models, the appropriate rewarding, and the realization of the underlying neural network. The paper describes vehicle models, simulation possibilities and computational requirements. Strategic decisions on different layers and the observation models, e.g., continuous and discrete state representations, grid-based, and camera-based solutions are presented. The paper surveys the state-of-art solutions systematized by the different tasks and levels of autonomous driving, such as car-following, lane-keeping, trajectory following, merging, or driving in dense traffic. Finally, open questions and future challenges are discussed.

Theoretical Interpretation of Learned Step Size in Deep-Unfolded Gradient Descent Satoshi Takabe † and Tadashi Wadayama Nagoya Institute of Technology, Gokiso, Nagoya, Aichi, 466-8555, Japan, {wadayama, s_takabe}@nitech.ac.jp † RIKEN Center for Advanced Intelligence Project, Chuo-ku, Tokyo, 103-0027, Japan Abstract --Deep unfolding is a promising deep-learning technique in which an iterative algorithm is unrolled to a deep network architecture with trainable parameters. In the case of gradient descent algorithms, as a result of the training process, one often observes the acceleration of the convergence speed with learned non-constant step size parameters whose behavior is not intuitive nor interpretable from conventional theory. In this paper, we provide a theoretical interpretation of the learned step size of deep-unfolded gradient descent (DUGD). We first prove that the training process of DUGD reduces not only the mean squared error loss but also the spectral radius related to the convergence rate. Next, we show that minimizing the upper bound of the spectral radius naturally leads to the Chebyshev step which is a sequence of the step size based on Chebyshev polynomials. The numerical experiments confirm that the Chebyshev steps qualitatively reproduce the learned step size parameters in DUGD, which provides a plausible interpretation of the learned parameters. Additionally, we show that the Chebyshev steps achieve the lower bound of the convergence rate for the first-order method in a specific limit without learning parameters or momentum terms. I NTRODUCTION Deep unfolding [10], [12] is a promising deep learning approach whose architecture is based on existing iterative algorithms with tuning parameters such as step sizes in gradient descent (GD). The recursive structure of the algorithm is unrolled to a deep network and some parameters are embedded into the network. These parameters can be trained using standard deep learning techniques such as back propagation and stochastic GD if all the processes in the algorithm are differentiable. One notable advantage of deep unfolding is the acceleration of the convergence speed that results from tuning parameters compared with the original algorithm. Embedding proper trainable parameters also offers a flexible network structure to the algorithm that is applicable, for example, to inverse problems with/without prior information [26]. Recently, theoretical aspects of deep unfolding have also been investigated [5], [21], [23]. MSE performance (upper) and learned step size parameters {γ t} 24 t 0 (lower) of DUGD (circles) and GD with a constant step size (cross marks) when (n,m) (300, 600).

LEARNING PERCEPTION AND PLANNING WITH DEEP ACTIVE INFERENCE Ozan C atal Tim V erbelen Johannes Nauta Cedric De Boom Bart Dhoedt IDLab Department of Information Technology at Ghent University - imec ABSTRACT Active inference is a process theory of the brain that states that all living organisms infer actions in order to minimize their (expected) free energy. However, current experiments are limited to predefined, often discrete, state spaces. In this paper we use recent advances in deep learning to learn the state space and approximate the necessary probability distributions to engage in active inference. Index T erms -- active inference, deep learning, perception, planning 1. INTRODUCTION Active inference postulates that action selection in biological systems, in particular the human brain, is actually an inference problem where agents are attracted to a preferred prior state distribution in a hidden state space [1]. To do so, each living organism builds an internal generative model of the world, by minimizing the so-called free energy.

Graphs can be used to represent and reason about real world systems. A variety of metrics have been devised to quantify their global characteristics. In general, prior work focuses on measuring the properties of existing graphs rather than the problem of dynamically modifying them (for example, by adding edges) in order to improve the value of an objective function. In this paper, we present RNet-DQN, a solution for improving graph robustness based on Graph Neural Network architectures and Deep Reinforcement Learning. We investigate the application of this approach for improving graph robustness, which is relevant to infrastructure and communication networks. We capture robustness using two objective functions and use changes in their values as the reward signal. Our experiments show that our approach can learn edge addition policies for improving robustness that perform significantly better than random and, in some cases, exceed the performance of a greedy baseline. Crucially, the learned policies generalize to different graphs including those larger than the ones on which they were trained. This is important because the naive greedy solution can be prohibitively expensive to compute for large graphs; our approach offers an $O(|V|^3)$ speed-up with respect to it.

Deep reinforcement learning (RL) has achieved outstanding results in recent years, which has led a dramatic increase in the number of methods and applications. Recent works are exploring learning beyond single-agent scenarios and considering multi-agent scenarios. However, they are faced with lots of challenges and are seeking for help from traditional game-theoretic algorithms, which, in turn, show bright application promise combined with modern algorithms and boosting computing power. In this survey, we first introduce basic concepts and algorithms in single agent RL and multi-agent systems; then, we summarize the related algorithms from three aspects. Solution concepts from game theory give inspiration to algorithms which try to evaluate the agents or find better solutions in multi-agent systems. Fictitious self-play becomes popular and has a great impact on the algorithm of multi-agent reinforcement learning. Counterfactual regret minimization is an important tool to solve games with incomplete information, and has shown great strength when combined with deep learning.