A general tension-reduction (GTR) model was recently considered to derive quantum probabilities as (universal) averages over all possible forms of non-uniform fluctuations, and explain their considerable success in describing experimental situations also outside of the domain of physics, for instance in the ambit of quantum models of cognition and decision. Yet, this result also highlighted the possibility of observing violations of the predictions of the Born rule, in those situations where the averaging would not be large enough, or would be altered because of the combination of multiple measurements. In this article we show that this is indeed the case in typical psychological measurements exhibiting question order effects, by showing that their statistics of outcomes are inherently non-Hilbertian, and require the larger framework of the GTR-model to receive an exact mathematical description. We also consider another unsolved problem of quantum cognition: response replicability. It is has been observed that when question order effects and response replicability occur together, the situation cannot be handled anymore by quantum theory. However, we show that it can be easily and naturally described in the GTR-model. Based on these findings, we motivate the adoption in cognitive science of a hidden-measurements interpretation of the quantum formalism, and of its GTR-model generalization, as the natural interpretational framework explaining the data of psychological measurements on conceptual entities.

Compared to conventional cars, electric vehicles (EVs) still suffer from considerably shorter cruising ranges. Combined with the sparsity of battery loading stations, the complete transition to E-mobility still seems a long way to go. In this paper, we consider the problem of placing as few loading stations as possible so that on any shortest path there are sufficiently many not to run out of energy. We show how to model this problem and introduce heuristics which provide close-to-optimal solutions even in large road networks.

Dropout has recently emerged as a powerful and simple method for training neural networks preventing co-adaptation by stochastically omitting neurons. Dropout is currently not grounded in explicit modelling assumptions which so far has precluded its adoption in Bayesian modelling. Using Bayesian entropic reasoning we show that dropout can be interpreted as optimal inference under constraints. We demonstrate this on an analytically tractable regression model providing a Bayesian interpretation of its mechanism for regularizing and preventing co-adaptation as well as its connection to other Bayesian techniques. We also discuss two general approximate techniques for applying Bayesian dropout for general models, one based on an analytical approximation and the other on stochastic variational techniques. These techniques are then applied to a Baysian logistic regression problem and are shown to improve performance as the model become more misspecified. Our framework roots dropout as a theoretically justified and practical tool for statistical modelling allowing Bayesians to tap into the benefits of dropout training.

There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding large independent sets in sparse random regular graphs. Montanari (2015) showed that local algorithms are suboptimal for finding a community with high connectivity in the sparse Erd\H{o}s-R\'enyi random graphs. For the symmetric planted partition problem (also named community detection for the block models) on sparse graphs, a simple observation is that local algorithms cannot have non-trivial performance. In this work we consider the effect of side information on local algorithms for community detection under the binary symmetric stochastic block model. In the block model with side information each of the $n$ vertices is labeled $+$ or $-$ independently and uniformly at random; each pair of vertices is connected independently with probability $a/n$ if both of them have the same label or $b/n$ otherwise. The goal is to estimate the underlying vertex labeling given 1) the graph structure and 2) side information in the form of a vertex labeling positively correlated with the true one. Assuming that the ratio between in and out degree $a/b$ is $\Theta(1)$ and the average degree $ (a+b) / 2 = n^{o(1)}$, we characterize three different regimes under which a local algorithm, namely, belief propagation run on the local neighborhoods, maximizes the expected fraction of vertices labeled correctly. Thus, in contrast to the case of symmetric block models without side information, we show that local algorithms can achieve optimal performance for the block model with side information.

Technology offers new ways to measure the locations of the players and of the ball in sports. This translates to the trajectories the ball takes on the field as a result of the tactics the team applies. The challenge professionals in soccer are facing is to take the reverse path: given the trajectories of the ball is it possible to infer the underlying strategy/tactic of a team? We propose a method based on Dynamic Time Warping to reveal the tactics of a team through the analysis of repeating series of events. Based on the analysis of an entire season, we derive insights such as passing strategies for maintaining ball possession or counter attacks, and passing styles with a focus on the team or on the capabilities of the individual players.

A new dimension reduction method based on Gaussian finite mixtures is proposed as an extension to sliced inverse regression (SIR). The model-based SIR (MSIR) approach allows the main limitation of SIR to be overcome, i.e., failure in the presence of regression symmetric relationships, without the need to impose further assumptions. Extensive numerical studies are presented to compare the new method with some of most popular dimension reduction methods, such as SIR, sliced average variance estimation, principal Hessian direction, and directional regression. MSIR appears sufficiently flexible to accommodate various regression functions, and its performance is comparable with or better, particularly as sample size grows, than other available methods. Lastly, MSIR is illustrated with two real data examples about ozone concentration regression, and hand-written digit classification.

This paper discusses several problems in dynamical systems and control, where methods from learning theory are used in the state space of linear systems. This is in contrast to previous approaches in the frequency domain [19, 6]. We refer to [6] for a general survey on applications of machine learning to system identification. Basically, learning theory allows to deal with problems when only data from a given system are given. Reproducing Kernel Hilbert Spaces (RKHS) allow to work in a very large dimensional space in order to simplify the underlying problem.

This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. We investigate the spectral convergence of both unnormalized and normalized graph Laplacians towards the appropriate operators in the continuum domain. We obtain sharp conditions on how the connectivity radius can be scaled with respect to the number of sample points for the spectral convergence to hold. We also show that the discrete clusters obtained via spectral clustering converge towards a continuum partition of the ground truth measure. Such continuum partition minimizes a functional describing the continuum analogue of the graph-based spectral partitioning. Our approach, based on variational convergence, is general and flexible.

Decadal climate predictions, which are initialized with observed conditions, are characterized by two main sources of uncertainties--internal and model variabilities. Using an ensemble of climate model simulations from the CMIP5 decadal experiments, we quantified the total uncertainty associated with these predictions and the relative importance of each source. Annual and monthly averages of the surface temperature and wind components were considered. We show that different definitions of the anomaly results in different conclusions regarding the variance of the ensemble members. However, some features of the uncertainty are common to all the measures we considered. We found that over decadal time scales, there is no considerable increase in the uncertainty with time. The model variability is more sensitive to the annual cycle than the internal variability. This, in turn, results in a maximal uncertainty during the winter in the northern hemisphere. The uncertainty of the surface temperature prediction is dominated by the model variability, whereas the uncertainty of the wind components is determined by both sources. Analysis of the spatial distribution of the uncertainty reveals that the surface temperature has higher variability over land and in high latitudes, whereas the surface zonal wind has higher variability over the ocean. The relative importance of the internal and model variabilities depends on the averaging period, the definition of the anomaly, and the location. These findings suggest that several methods should be combined in order to assess future climate prediction uncertainties and that weighting schemes of the ensemble members may reduce the uncertainties.

With the recent availability of much network data, such as world wide web, social networks, phone call networks, science collaboration graphs [1], [2], there is a renewed interest for the graph partitioning problem, especially for the automatic discovery of community structures in large networks [3], [4], [5]. Beyond clustering approaches, coclustering approaches aim at summarizing the relation between two entities in a many-to-many relationship. Such a relation can be represented as a graph, where the source and target vertices represent entities and the edges stand for relations between entities. A coclustering model provides a summary of a graph by grouping source vertices and target vertices. For example, in market analysis, the source vertices of the graph represent customers, the target vertices represent products and there is one edge each time a customer has purchased a product. A coclustering model summarizes the dataset by grouping customers that have purchased approximately the same products and grouping products that have been purchased by approximately the same customers. Coclustering models have been applied to many other domains, such as information retrieval (the entities are documents and their words in a text corpus), web log analysis (cookies and their visited web pages), web structure analysis (web pages with hyperlinks between them) or telecommunication network (the call detail records stand for the edges in a call graph between a caller and a called party). All these real-world graphs are directed multigraphs, meaning that two entities may be linked by multi-edges. We aim to summarize and discover insightful patterns in such graphs, using a method with the desired following properties: 1) Robustness, to avoid detecting spurious patterns in case of noisy data.