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We investigate a family of rule-based logics. The focus is on very expressive languages. We provide a range of characterization results for the expressive powers of the logics and relate them with corresponding game systems.

It is well established that migratory birds in general have advanced their arrival times in spring, and in this paper we investigate potential ways of enhancing the level of detail in future phenological analyses. We perform single as well as multiple species analyses, using linear models on empirical quantiles, non-parametric quantile regression and likelihood-based parametric quantile regression with asymmetric Laplace distributed error terms. We conclude that non-parametric quantile regression appears most suited for single as well as multiple species analyses.

[Context] Open Source Software (OSS) is nowadays used and integrated in most of the commercial products. However, the selection of OSS projects for integration is not a simple process, mainly due to a of lack of clear selection models and lack of information from the OSS portals. [Objective] We investigate the factors and metrics that practitioners currently consider when selecting OSS. We also investigate the source of information and portals that can be used to assess the factors, as well as the possibility to automatically extract such information with APIs. [Method] We elicited the factors and the metrics adopted to assess and compare OSS performing a survey among 23 experienced developers who often integrate OSS in the software they develop. Moreover, we investigated the APIs of the portals adopted to assess OSS extracting information for the most starred 100K projects in GitHub. [Result] We identified a set consisting of 8 main factors and 74 sub-factors, together with 170 related metrics that companies can use to select OSS to be integrated in their software projects. Unexpectedly, only a small part of the factors can be evaluated automatically, and out of 170 metrics, only 40 are available, of which only 22 returned information for all the 100K projects. Therefore, we recommend project maintainers and project repositories to pay attention to provide information for the project they are hosting, so as to increase the likelihood of being adopted [Conclusion] OSS selection can be partially automated, by extracting the information needed for the selection from portal APIs. OSS producers can benefit from our results by checking if they are providing all the information commonly required by potential adopters...

Causal discovery, the learning of causality in a data mining scenario, has been of strong scientific and theoretical interest as a starting point to identify "what causes what?" Contingent on assumptions, it is sometimes possible to identify an exact causal Directed Acyclic Graph (DAG), as opposed to a Markov equivalence class of graphs that gives ambiguity of causal directions. The focus of this paper is on one such case: a linear structural equation model with non-Gaussian noise, a model known as the Linear Non-Gaussian Acyclic Model (LiNGAM). Given a specified parametric noise model, we develop a novel sequential approach to estimate the causal ordering of a DAG. At each step of the procedure, only simple likelihood ratio scores are calculated on regression residuals to decide the next node to append to the current partial ordering. Under mild assumptions, the population version of our procedure provably identifies a true ordering of the underlying causal DAG. We provide extensive numerical evidence to demonstrate that our sequential procedure is scalable to cases with possibly thousands of nodes and works well for high-dimensional data. We also conduct an application to a single-cell gene expression dataset to demonstrate our estimation procedure.

The main purpose of this paper is to introduce a new class of regression models for bounded continuous data, commonly encountered in applied research. The models, named the power logit regression models, assume that the response variable follows a distribution in a wide, flexible class of distributions with three parameters, namely the median, a dispersion parameter and a skewness parameter. The paper offers a comprehensive set of tools for likelihood inference and diagnostic analysis, and introduces the new R package PLreg. Applications with real and simulated data show the merits of the proposed models, the statistical tools, and the computational package.

While in recent years a number of new statistical approaches have been proposed to model group differences with a different assumption on the nature of the measurement invariance of the instruments, the tools for detecting local misspecifications of these models have not been fully developed yet. In this study, we present a novel approach using a Deep Neural Network (DNN). We compared the proposed model with the most popular traditional methods: Modification Indices (MI) and Expected Parameter Change (EPC) indicators from the Confirmatory Factor Analysis (CFA) modeling, logistic DIF detection, and sequential procedure introduced with the CFA alignment approach. Simulation studies show that the proposed method outperformed traditional methods in almost all scenarios, or it was at least as accurate as the best one. We also provide an empirical example utilizing European Social Survey data including items known to be miss-translated, which are correctly identified with presented DNN approach.

We present a simulation-based approach for solution of mean field games (MFGs), using the framework of empirical game-theoretical analysis (EGTA). Our method employs a version of the double oracle, iteratively adding strategies based on best response to the equilibrium of the empirical MFG among strategies considered so far. The empirical game equilibrium is computed with a query-based method, rather than maintaining an explicit payoff matrix as in typical EGTA methods. We show that NE exist in the empirical MFG and study the convergence of iterative EGTA to NE of the full MFG. We test the performance of iterative EGTA in various games and show that it outperforms in terms of iterations of strategy introduction. Finally, we discuss the limitations of applying iterative EGTA to MFGs as well as potential future research directions.

Exponential tail bounds for sums play an important role in statistics, but the example of the $t$-statistic shows that the exponential tail decay may be lost when population parameters need to be estimated from the data. However, it turns out that if Studentizing is accompanied by estimating the location parameter in a suitable way, then the $t$-statistic regains the exponential tail behavior. Motivated by this example, the paper analyzes other ways of empirically standardizing sums and establishes tail bounds that are sub-Gaussian or even closer to normal for the following settings: Standardization with Studentized contrasts for normal observations, standardization with the log likelihood ratio statistic for observations from an exponential family, and standardization via self-normalization for observations from a symmetric distribution with unknown center of symmetry. The latter standardization gives rise to a novel scan statistic for heteroscedastic data whose asymptotic power is analyzed in the case where the observations have a log-concave distribution.

We investigate properties of goodness-of-fit tests based on the Kernel Stein Discrepancy (KSD). We introduce a strategy to construct a test, called KSDAgg, which aggregates multiple tests with different kernels. KSDAgg avoids splitting the data to perform kernel selection (which leads to a loss in test power), and rather maximises the test power over a collection of kernels. We provide theoretical guarantees on the power of KSDAgg: we show it achieves the smallest uniform separation rate of the collection, up to a logarithmic term. KSDAgg can be computed exactly in practice as it relies either on a parametric bootstrap or on a wild bootstrap to estimate the quantiles and the level corrections. In particular, for the crucial choice of bandwidth of a fixed kernel, it avoids resorting to arbitrary heuristics (such as median or standard deviation) or to data splitting. We find on both synthetic and real-world data that KSDAgg outperforms other state-of-the-art adaptive KSD-based goodness-of-fit testing procedures.

We investigate how the final parameters found by stochastic gradient descent are influenced by over-parameterization. We generate families of models by increasing the number of channels in a base network, and then perform a large hyper-parameter search to study how the test error depends on learning rate, batch size, and network width. We find that the optimal SGD hyper-parameters are determined by a "normalized noise scale," which is a function of the batch size, learning rate, and initialization conditions. In the absence of batch normalization, the optimal normalized noise scale is directly proportional to width. Wider networks, with their higher optimal noise scale, also achieve higher test accuracy. These observations hold for MLPs, ConvNets, and ResNets, and for two different parameterization schemes ("Standard" and "NTK"). We observe a similar trend with batch normalization for ResNets. Surprisingly, since the largest stable learning rate is bounded, the largest batch size consistent with the optimal normalized noise scale decreases as the width increases.