Modern machine learning models are often over-parameterized and as a result they can interpolate the training data. Under such a scenario, we study the convergence properties of a sampling-without-replacement variant of stochastic gradient descent (SGD) known as random reshuffling (RR). Unlike SGD that samples data with replacement at every iteration, RR chooses a random permutation of data at the beginning of each epoch and each iteration chooses the next sample from the permutation. For under-parameterized models, it has been shown RR can converge faster than SGD under certain assumptions. However, previous works do not show that RR outperforms SGD in over-parameterized settings except in some highly-restrictive scenarios. For the class of Polyak-\L ojasiewicz (PL) functions, we show that RR can outperform SGD in over-parameterized settings when either one of the following holds: (i) the number of samples ($n$) is less than the product of the condition number ($\kappa$) and the parameter ($\alpha$) of a weak growth condition (WGC), or (ii) $n$ is less than the parameter ($\rho$) of a strong growth condition (SGC).

Ontology-based clustering has gained attention in recent years due to the potential benefits of ontology. Current ontology-based clustering approaches have mainly been applied to reduce the dimensionality of attributes in text document clustering. Reduction in dimensionality of attributes using ontology helps to produce high quality clusters for a dataset. However, ontology-based approaches in clustering numerical datasets have not been gained enough attention. Moreover, some literature mentions that ontology-based clustering can produce either high quality or low-quality clusters from a dataset. Therefore, in this paper we present a clustering approach that is based on domain ontology to reduce the dimensionality of attributes in a numerical dataset using domain ontology and to produce high quality clusters. For every dataset, we produce three datasets using domain ontology. We then cluster these datasets using a genetic algorithm-based clustering technique called GenClust++. The clusters of each dataset are evaluated in terms of Sum of Squared-Error (SSE). We use six numerical datasets to evaluate the performance of our ontology-based approach. The experimental results of our approach indicate that cluster quality gradually improves from lower to the higher levels of a domain ontology.

Comparison-based learning addresses the problem of learning when, instead of explicit features or pairwise similarities, one only has access to comparisons of the form: \emph{Object $A$ is more similar to $B$ than to $C$.} Recently, it has been shown that, in Hierarchical Clustering, single and complete linkage can be directly implemented using only such comparisons while several algorithms have been proposed to emulate the behaviour of average linkage. Hence, finding hierarchies (or dendrograms) using only comparisons is a well understood problem. However, evaluating their meaningfulness when no ground-truth nor explicit similarities are available remains an open question. In this paper, we bridge this gap by proposing a new revenue function that allows one to measure the goodness of dendrograms using only comparisons. We show that this function is closely related to Dasgupta's cost for hierarchical clustering that uses pairwise similarities. On the theoretical side, we use the proposed revenue function to resolve the open problem of whether one can approximately recover a latent hierarchy using few triplet comparisons. On the practical side, we present principled algorithms for comparison-based hierarchical clustering based on the maximisation of the revenue and we empirically compare them with existing methods.

An ever-growing number of vulnerabilities are reported every day. Yet these vulnerabilities are not all the same; Some are more targeted than others. Correctly estimating the likelihood of a vulnerability being exploited is a critical task for system administrators. This aids the system administrators in prioritizing and patching the right vulnerabilities. Our work makes use of outlier detection techniques to predict vulnerabilities that are likely to be exploited in highly imbalanced and high-dimensional datasets such as the National Vulnerability Database. We propose a dimensionality reduction technique, OutCenTR, that enhances the baseline outlier detection models. We further demonstrate the effectiveness and efficiency of OutCenTR empirically with 4 benchmark and 12 synthetic datasets. The results of our experiments show on average a 5-fold improvement of F1 score in comparison with state-of-the-art dimensionality reduction techniques such as PCA and GRP.

Abnormal event detection, which refers to mining unusual interactions among involved entities, plays an important role in many real applications. Previous works mostly over-simplify this task as detecting abnormal pair-wise interactions. However, real-world events may contain multi-typed attributed entities and complex interactions among them, which forms an Attributed Heterogeneous Information Network (AHIN). With the boom of social networks, abnormal event detection in AHIN has become an important, but seldom explored task. In this paper, we firstly study the unsupervised abnormal event detection problem in AHIN. The events are considered as star-schema instances of AHIN and are further modeled by hypergraphs. A novel hypergraph contrastive learning method, named AEHCL, is proposed to fully capture abnormal event patterns. AEHCL designs the intra-event and inter-event contrastive modules to exploit self-supervised AHIN information. The intra-event contrastive module captures the pair-wise and multivariate interaction anomalies within an event, and the inter-event module captures the contextual anomalies among events. These two modules collaboratively boost the performance of each other and improve the detection results. During the testing phase, a contrastive learning-based abnormal event score function is further proposed to measure the abnormality degree of events. Extensive experiments on three datasets in different scenarios demonstrate the effectiveness of AEHCL, and the results improve state-of-the-art baselines up to 12.0% in Average Precision (AP) and 4.6% in Area Under Curve (AUC) respectively.

Zero-inflated continuous data ubiquitously appear in many fields, in which lots of exactly zero-valued data are observed while others distribute continuously. Due to the mixed structure of discreteness and continuity in its distribution, statistical analysis is challenging especially for multivariate case. In this paper, we propose two copula-based density estimation models that can cope with multivariate correlation among zero-inflated continuous variables. In order to overcome the difficulty in the use of copulas due to the tied-data problem in zero-inflated data, we propose a new type of copula, rectified Gaussian copula, and present efficient methods for parameter estimation and likelihood computation. Numerical experiments demonstrates the superiority of our proposals compared to conventional density estimation methods.

We are interested in estimating the effect of a treatment applied to individuals at multiple sites, where data is stored locally for each site. Due to privacy constraints, individual-level data cannot be shared across sites; the sites may also have heterogeneous populations and treatment assignment mechanisms. Motivated by these considerations, we develop federated methods to draw inference on the average treatment effects of combined data across sites. Our methods first compute summary statistics locally using propensity scores and then aggregate these statistics across sites to obtain point and variance estimators of average treatment effects. We show that these estimators are consistent and asymptotically normal. To achieve these asymptotic properties, we find that the aggregation schemes need to account for the heterogeneity in treatment assignments and in outcomes across sites. We demonstrate the validity of our federated methods through a comparative study of two large medical claims databases.

We derive high-dimensional scaling limits and fluctuations for the online least-squares Stochastic Gradient Descent (SGD) algorithm by taking the properties of the data generating model explicitly into consideration. Our approach treats the SGD iterates as an interacting particle system, where the expected interaction is characterized by the covariance structure of the input. Assuming smoothness conditions on moments of order up to eight orders, and without explicitly assuming Gaussianity, we establish the high-dimensional scaling limits and fluctuations in the form of infinite-dimensional Ordinary Differential Equations (ODEs) or Stochastic Differential Equations (SDEs). Our results reveal a precise three-step phase transition of the iterates; it goes from being ballistic, to diffusive, and finally to purely random behavior, as the noise variance goes from low, to moderate and finally to very-high noise setting. In the low-noise setting, we further characterize the precise fluctuations of the (scaled) iterates as infinite-dimensional SDEs. We also show the existence and uniqueness of solutions to the derived limiting ODEs and SDEs. Our results have several applications, including characterization of the limiting mean-square estimation or prediction errors and their fluctuations which can be obtained by analytically or numerically solving the limiting equations.

Abstract: Taking the goodness of fit test (Chi test) as an example, this paper attempts to calculate the Bayesian factor BF10 of n-fold Bernoulli test by the Excel software (using JASP software as the evidence). The results showed that in the range of 0.15–0.55 Abstract: The sensitivity of gravitational wave searches is reduced by the presence of non-Gaussian noise in the detector data. These non-Gaussianities often match well with the template waveforms used in matched filter searches, and require signal-consistency tests to distinguish them from astrophysical signals. However, empirically tuning these tests for maximum efficacy is time consuming and limits the complexity of these tests. In this work we demonstrate a framework to use machine-learning techniques to automatically tune signal-consistency tests.

Abstract: For many probability laws, in parametric models, the estimation of the parameters can be done in the frame of the maximum likelihood method, or in the frame of moment estimation methods, or by using the plug-in method, etc. Usually, for estimating more than one parameter, the same frame is used. We focus on the moment estimation method in this paper. We use the instrumental tool of the functional empirical process (fep) in Lo (2016) to show how it is practical to derive, almost algebraically, the joint distribution Gaussian law and to derive omnibus chi-square asymptotic laws from it. We choose four distributions to illustrate the method (Gamma law, beta law, Uniform law and Fisher law) and completely describe the asymptotic laws of the moment estimators whenever possible. Simulations studies are performed to investigate for each case the smallest sizes for which the obtained statistical tests are recommendable.