Computational social choice is a research area at the intersection of social choice (the science of collective decision-making) and computer science, which focuses on the algorithmic analysis of problems related topreference aggregation and elicitation(Brandt etal.,2013).

Our main contribution is the introduction of the map of elections framework. A map of elections consists of three main elements: (1) a dataset of elections (i.e., collections of ordinal votes over given sets of candidates), (2) a way of measuring similarities between these elections, and (3) a representation of the elections in the 2D Euclidean space as points, so that the more similar two elections are, the closer are their points. In our maps, we mostly focus on datasets of synthetic elections, but we also show an example of a map over real-life ones. To measure similarities, we would have preferred to use, e.g., the isomorphic swap distance, but this is infeasible due to its high computational complexity. Hence, we propose polynomial-time computable positionwise distance and use it instead. Regarding the representations in 2D Euclidean space, we mostly use the Kamada-Kawai algorithm, but we also show two alternatives. We develop the necessary theoretical results to form our maps and argue experimentally that they are accurate and credible. Further, we show how coloring the elections in a map according to various criteria helps in analyzing results of a number of experiments. In particular, we show colorings according to the scores of winning candidates or committees, running times of ILP-based winner determination algorithms, and approximation ratios achieved by particular algorithms.

We use the "map of elections" approach of Szufa et al. (AAMAS 2020) to analyze several well-known vote distributions. For each of them, we give an explicit formula or an efficient algorithm for computing its frequency matrix, which captures the probability that a given candidate appears in a given position in a sampled vote. We use these matrices to draw the "skeleton map" of distributions, evaluate its robustness, and analyze its properties. We further develop a general and unified framework for learning the distribution of real-world preferences using the frequency matrices of established vote distributions.

With the development of society, time series anomaly detection plays an important role in network and IoT services. However, most existing anomaly detection methods directly analyze time series in the time domain and cannot distinguish some relatively hidden anomaly sequences. We attempt to analyze the impact of frequency on time series from a frequency domain perspective, thus proposing a new time series anomaly detection method called F-SE-LSTM. This method utilizes two sliding windows and fast Fourier transform (FFT) to construct a frequency matrix. Simultaneously, Squeeze-and-Excitation Networks (SENet) and Long Short-Term Memory (LSTM) are employed to extract frequency-related features within and between periods. Through comparative experiments on multiple datasets such as Yahoo Webscope S5 and Numenta Anomaly Benchmark, the results demonstrate that the frequency matrix constructed by F-SE-LSTM exhibits better discriminative ability than ordinary time domain and frequency domain data. Furthermore, F-SE-LSTM outperforms existing state-of-the-art deep learning anomaly detection methods in terms of anomaly detection capability and execution efficiency.

In sufficiently complex tasks, it is expected that as a side effect of learning to solve a problem, a neural network will learn relevant abstractions of the representation of that problem. This has been confirmed in particular in machine vision where a number of works showed that correlations could be found between the activations of specific units (neurons) in a neural network and the visual concepts (textures, colors, objects) present in the image. Here, we explore the use of self-organizing maps as a way to both visually and computationally inspect how activation vectors of whole layers of neural networks correspond to neural representations of abstract concepts such as `female person' or `realist painter'. We experiment with multiple measures applied to those maps to assess the level of representation of a concept in a network's layer. We show that, among the measures tested, the relative entropy of the activation map for a concept compared to the map for the whole data is a suitable candidate and can be used as part of a methodology to identify and locate the neural representation of a concept, visualize it, and understand its importance in solving the prediction task at hand.

We use the ``map of elections'' approach of Szufa et al. (AAMAS-2020) to analyze several well-known vote distributions. For each of them, we give an explicit formula or an efficient algorithm for computing its frequency matrix, which captures the probability that a given candidate appears in a given position in a sampled vote. We use these matrices to draw the ``skeleton map'' of distributions, evaluate its robustness, and analyze its properties. Finally, we develop a general and unified framework for learning the distribution of real-world preferences using the frequency matrices of established vote distributions.

The ability to accurately predict the fit of fashion items and recommend the correct size is key to reducing merchandise returns in e-commerce. A critical prerequisite of fit prediction is size normalization, the mapping of product sizes across brands to a common space in which sizes can be compared. At present, size normalization is usually a time-consuming manual process. We propose a method to automate size normalization through the use of salesdata. The size mappings generated from our automated approaches are comparable to human-generated mappings.

Dimension reduction is a central problem in system engineering and data science. In scientific studies or engineering applications, one often needs to interact with unknown complex systems about which many noisy observations of system characteristics and system trajectories are available. The exact structures and dynamics of the system are typically masked by massive observations of noisy variables, many of which might not be relevant to the physical state of the system. It is often unclear how to describe the "state" of a system, when one can only access noisy observations. One may view each unique observation as a single state, however, this would generate a huge-or even infinite-dimensional process which is difficult to model or analyze. Although there exists a vast body of literatures on time series analysis [18], they typically require knowledge of specific models and might perform poorly when the models are misspecified. Anru Zhang is Assistant Professor, Department of Statistics, University of Wisconsin-Madison, Madison, WI 53706, Email: anruzhang@stat.wisc.edu; Mengdi Wang is Assistant Professor, Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544, Email: mengdiw@princeton.edu.