Screening rules allow to early discard irrelevant variables from the optimization in Lasso problems, or its derivatives, making solvers faster. In this paper, we propose new versions of the so-called $\textit{safe rules}$ for the Lasso. Based on duality gap considerations, our new rules create safe test regions whose diameters converge to zero, provided that one relies on a converging solver. This property helps screening out more variables, for a wider range of regularization parameter values. In addition to faster convergence, we prove that we correctly identify the active sets (supports) of the solutions in finite time. While our proposed strategy can cope with any solver, its performance is demonstrated using a coordinate descent algorithm particularly adapted to machine learning use cases. Significant computing time reductions are obtained with respect to previous safe rules.

We present a very general geometrico-dynamical description of physical or more abstract entities, called the 'general tension-reduction' (GTR) model, where not only states, but also measurement-interactions can be represented, and the associated outcome probabilities calculated. Underlying the model is the hypothesis that indeterminism manifests as a consequence of unavoidable fluctuations in the experimental context, in accordance with the 'hidden-measurements interpretation' of quantum mechanics. When the structure of the state space is Hilbertian, and measurements are of the 'universal' kind, i.e., are the result of an average over all possible ways of selecting an outcome, the GTR-model provides the same predictions of the Born rule, and therefore provides a natural completed version of quantum mechanics. However, when the structure of the state space is non-Hilbertian and/or not all possible ways of selecting an outcome are available to be actualized, the predictions of the model generally differ from the quantum ones, especially when sequential measurements are considered. Some paradigmatic examples will be discussed, taken from physics and human cognition. Particular attention will be given to some known psychological effects, like question order effects and response replicability, which we show are able to generate non-Hilbertian statistics. We also suggest a realistic interpretation of the GTR-model, when applied to human cognition and decision, which we think could become the generally adopted interpretative framework in quantum cognition research.

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ball is chosen judiciously, we can guarantee that it contains the unknown data-generating distribution with high confidence. We then formulate a distributionally robust logistic regression model that minimizes a worst-case expected logloss function, where the worst case is taken over all distributions in the Wasserstein ball. We prove that this optimization problem admits a tractable reformulation and encapsulates the classical as well as the popular regularized logistic regression problems as special cases. We further propose a distributionally robust approach based on Wasserstein balls to compute upper and lower confidence bounds on the misclassification probability of the resulting classifier. These bounds are given by the optimal values of two highly tractable linear programs. We validate our theoretical out-of-sample guarantees through simulated and empirical experiments.

The understanding of the type of inhibitory interaction plays an important role in drug design. Therefore, researchers are interested to know whether a drug has competitive or non-competitive interaction to particular protein targets. Method: to analyze the interaction types we propose factorization method Macau which allows us to combine different measurement types into a single tensor together with proteins and compounds. The compounds are characterized by high dimensional 2D ECFP fingerprints. The novelty of the proposed method is that using a specially designed noise injection MCMC sampler it can incorporate high dimensional side information, i.e., millions of unique 2D ECFP compound features, even for large scale datasets of millions of compounds. Without the side information, in this case, the tensor factorization would be practically futile. Results: using public IC50 and Ki data from ChEMBL we trained a model from where we can identify the latent subspace separating the two measurement types (IC50 and Ki). The results suggest the proposed method can detect the competitive inhibitory activity between compounds and proteins.

Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This paper presents generalizations of such estimation error analysis on all four aspects compared to the existing literature. We characterize the restricted error set where the estimation error vector lies, establish relations between error sets for the constrained and regularized problems, and present an estimation error bound applicable to any norm. Precise characterizations of the bound is presented for isotropic as well as anisotropic subGaussian design matrices, subGaussian noise models, and convex loss functions, including least squares and generalized linear models. Generic chaining and associated results play an important role in the analysis. A key result from the analysis is that the sample complexity of all such estimators depends on the Gaussian width of a spherical cap corresponding to the restricted error set. Further, once the number of samples $n$ crosses the required sample complexity, the estimation error decreases as $\frac{c}{\sqrt{n}}$, where $c$ depends on the Gaussian width of the unit norm ball.

Most ethical work is done at a low level of formality. This makes practical moral questions inaccessible to formal and natural sciences and can lead to misunderstandings in ethical discussion. In this paper, we use Bayesian inference to introduce a formalization of preference utilitarianism in physical world models, specifically cellular automata. Even though our formalization is not immediately applicable, it is a first step in providing ethics and ultimately the question of how to "make the world better" with a formal basis.

Automated sentiment analysis and opinion mining is a complex process concerning the extraction of useful subjective information from text. The explosion of user generated content on the Web, especially the fact that millions of users, on a daily basis, express their opinions on products and services to blogs, wikis, social networks, message boards, etc., render the reliable, automated export of sentiments and opinions from unstructured text crucial for several commercial applications. In this paper, we present a novel hybrid vectorization approach for textual resources that combines a weighted variant of the popular Word2Vec representation (based on Term Frequency-Inverse Document Frequency) representation and with a Bag- of-Words representation and a vector of lexicon-based sentiment values. The proposed text representation approach is assessed through the application of several machine learning classification algorithms on a dataset that is used extensively in literature for sentiment detection. The classification accuracy derived through the proposed hybrid vectorization approach is higher than when its individual components are used for text represenation, and comparable with state-of-the-art sentiment detection methodologies.

In this paper, we present a board game: Square War. The game definition of Square War is similar to the classic Chinese board game Go. Then we propose a mathematical problem of the game Square War. Finally, we show that the problem can be solved by using a method of mixed mathematics and computer science.

The $k$-nearest neighbour ($k$-NN) classifier is one of the oldest and most important supervised learning algorithms for classifying datasets. Traditionally the Euclidean norm is used as the distance for the $k$-NN classifier. In this thesis we investigate the use of alternative distances for the $k$-NN classifier. We start by introducing some background notions in statistical machine learning. We define the $k$-NN classifier and discuss Stone's theorem and the proof that $k$-NN is universally consistent on the normed space $R^d$. We then prove that $k$-NN is universally consistent if we take a sequence of random norms (that are independent of the sample and the query) from a family of norms that satisfies a particular boundedness condition. We extend this result by replacing norms with distances based on uniformly locally Lipschitz functions that satisfy certain conditions. We discuss the limitations of Stone's lemma and Stone's theorem, particularly with respect to quasinorms and adaptively choosing a distance for $k$-NN based on the labelled sample. We show the universal consistency of a two stage $k$-NN type classifier where we select the distance adaptively based on a split labelled sample and the query. We conclude by giving some examples of improvements of the accuracy of classifying various datasets using the above techniques.

Computerized adaptive testing (CAT) is an interesting and promising approach to testing human abilities. In our research we use Bayesian networks to create a model of tested humans. We collected data from paper tests performed with grammar school students. In this article we first provide the summary of data used for our experiments. We propose several different Bayesian networks, which we tested and compared by cross-validation. Interesting results were obtained and are discussed in the paper. The analysis has brought a clearer view on the model selection problem. Future research is outlined in the concluding part of the paper.