Inference in the presence of outliers is an important field of research as outliers are ubiquitous and may arise across a variety of problems and domains. Bayesian optimization is method that heavily relies on probabilistic inference. This allows outstanding sample efficiency because the probabilistic machinery provides a memory of the whole optimization process. However, that virtue becomes a disadvantage when the memory is populated with outliers, inducing bias in the estimation. In this paper, we present an empirical evaluation of Bayesian optimization methods in the presence of outliers. The empirical evidence shows that Bayesian optimization with robust regression often produces suboptimal results. We then propose a new algorithm which combines robust regression (a Gaussian process with Student-t likelihood) with outlier diagnostics to classify data points as outliers or inliers. By using an scheduler for the classification of outliers, our method is more efficient and has better convergence over the standard robust regression. Furthermore, we show that even in controlled situations with no expected outliers, our method is able to produce better results.

Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether regression assumptions are met. Most traditional approaches require human decisions at this step, for example, the user adding or removing a variable until a satisfactory model is obtained. However, this trial-and-error strategy cannot guarantee that a subset that minimizes the errors while satisfying all regression assumptions will be found. In this paper, we propose a fully automated model building procedure for multiple linear regression subset selection that integrates model building and validation based on mathematical programming. The proposed model minimizes mean squared errors while ensuring that the majority of the important regression assumptions are met. When no subset satisfies all of the considered regression assumptions, our model provides an alternative subset that satisfies most of these assumptions. Computational results show that our model yields better solutions (i.e., satisfying more regression assumptions) compared to benchmark models while maintaining similar explanatory power.

Class imbalance classification is a challenging research problem in data mining and machine learning, as most of the real-life datasets are often imbalanced in nature. Existing learning algorithms maximise the classification accuracy by correctly classifying the majority class, but misclassify the minority class. However, the minority class instances are representing the concept with greater interest than the majority class instances in real-life applications. Recently, several techniques based on sampling methods (under-sampling of the majority class and over-sampling the minority class), cost-sensitive learning methods, and ensemble learning have been used in the literature for classifying imbalanced datasets. In this paper, we introduce a new clustering-based under-sampling approach with boosting (AdaBoost) algorithm, called CUSBoost, for effective imbalanced classification. The proposed algorithm provides an alternative to RUSBoost (random under-sampling with AdaBoost) and SMOTEBoost (synthetic minority over-sampling with AdaBoost) algorithms. We evaluated the performance of CUSBoost algorithm with the state-of-the-art methods based on ensemble learning like AdaBoost, RUSBoost, SMOTEBoost on 13 imbalance binary and multi-class datasets with various imbalance ratios. The experimental results show that the CUSBoost is a promising and effective approach for dealing with highly imbalanced datasets.

In this paper, we propose a mixture of probabilistic partial canonical correlation analysis (MPPCCA) that extracts the Causal Patterns from two multivariate time series. Causal patterns refer to the signal patterns within interactions of two elements having multiple types of mutually causal relationships, rather than a mixture of simultaneous correlations or the absence of presence of a causal relationship between the elements. In multivariate statistics, partial canonical correlation analysis (PCCA) evaluates the correlation between two multivariates after subtracting the effect of the third multivariate. PCCA can calculate the Granger Causal- ity Index (which tests whether a time-series can be predicted from an- other time-series), but is not applicable to data containing multiple partial canonical correlations. After introducing the MPPCCA, we propose an expectation-maxmization (EM) algorithm that estimates the parameters and latent variables of the MPPCCA. The MPPCCA is expected to ex- tract multiple partial canonical correlations from data series without any supervised signals to split the data as clusters. The method was then eval- uated in synthetic data experiments. In the synthetic dataset, our method estimated the multiple partial canonical correlations more accurately than the existing method. To determine the types of patterns detectable by the method, experiments were also conducted on real datasets. The method estimated the communication patterns In motion-capture data. The MP- PCCA is applicable to various type of signals such as brain signals, human communication and nonlinear complex multibody systems.

Noname manuscript No. (will be inserted by the editor) Abstract Predictive business process monitoring is concerned with the analysis of events produced during the execution of a business process in order to predict as early as possible the final outcome of an ongoing case. Traditionally, predictive process monitoring methods are optimized with respect to accuracy. However, in environments where users make decisions and take actions in response to the predictions they receive, it is equally important to optimize the stability of the successive predictions made for each case. To this end, this paper defines a notion of temporal stability for predictive process monitoring and evaluates existing methods with respect to both temporal stability and accuracy. We find that methods based on XGBoost and LSTM neural networks exhibit the highest temporal stability. We then show that temporal stability can be enhanced by hyperparameter-optimizing random forests and XGBoost classifiers with respect to inter-run stability. Finally, we show that time series smoothing techniques can further enhance temporal stability at the expense of slightly lower accuracy. Keywords Predictive Monitoring · Early Sequence Classification · Stability 1 Introduction Modern organizations generally execute their business processes on top of processaware information systems, such as Enterprise Resource Planning (ERP) systems, Customer Relationship Management (CRM) systems, and Business Process Management Systems (BPMS), among others [8]. These systems record a range of events that occur during the execution of the processes they support, including events signaling the creation and completion of business process instances (herein called cases) and the start and completion of activities within each case. Event records produced by process-aware information systems can be extracted and pre-processed to produce business process event logs [1]. A business process event log consists of a set of traces, each trace consisting of the sequence of event records produced by one case. Each event record has a number of attributes. Three of these attributes are present in every event record, namely the event class (a.k.a. In other words, every event represents the occurrence of an activity at a particular point in time and in the context of a given case.

We present a generative framework for generalized zero-shot learning where the training and test classes are not necessarily disjoint. Built upon a variational autoencoder based architecture, consisting of a probabilistic encoder and a probabilistic conditional decoder, our model can generate novel exemplars from seen/unseen classes, given their respective class attributes. These exemplars can subsequently be used to train any off-the-shelf classification model. One of the key aspects of our encoder-decoder architecture is a feedback-driven mechanism in which a discriminator (a multivariate regressor) learns to map the generated exemplars to the corresponding class attribute vectors, leading to an improved generator. Our model's ability to generate and leverage examples from unseen classes to train the classification model naturally helps to mitigate the bias towards predicting seen classes in generalized zero-shot learning settings. Through a comprehensive set of experiments, we show that our model outperforms several state-of-the-art methods, on several benchmark datasets, for both standard as well as generalized zero-shot learning.

Learning from class-imbalanced data continues to be a common and challenging problem in supervised learning as standard classification algorithms are designed to handle balanced class distributions. While different strategies exist to tackle this problem, methods which generate artificial data to achieve a balanced class distribution are more versatile than modifications to the classification algorithm. Such techniques, called oversamplers, modify the training data, allowing any classifier to be used with class-imbalanced datasets. Many algorithms have been proposed for this task, but most are complex and tend to generate unnecessary noise. This work presents a simple and effective oversampling method based on k-means clustering and SMOTE oversampling, which avoids the generation of noise and effectively overcomes imbalances between and within classes. Empirical results of extensive experiments with 71 datasets show that training data oversampled with the proposed method improves classification results. Moreover, k-means SMOTE consistently outperforms other popular oversampling methods. An implementation is made available in the python programming language.

There are many statistical tests that verify the null hypothesis: the variable of interest has the same distribution among k-groups. But once the null hypothesis is rejected, how to present the structure of dissimilarity between groups? In this article, we introduce The Merging Path Plot -- a methodology, and factorMerger -- an R package, for exploration and visualization of k-group dissimilarities. Comparison of k-groups is one of the most important issues in exploratory analyses and it has zillions of applications. The classical solution is to test a null hypothesis that observations from all groups come from the same distribution. If the global null hypothesis is rejected, a more detailed analysis of differences among pairs of groups is performed. The traditional approach is to use pairwise post hoc tests in order to verify which groups differ significantly. However, this approach fails with a large number of groups in both interpretation and visualization layer. The Merging Path Plot methodology solves this problem by using an easy-to-understand description of dissimilarity among groups based on Likelihood Ratio Test (LRT) statistic.

We study two procedures (reverse-mode and forward-mode) for computing the gradient of the validation error with respect to the hyperparameters of any iterative learning algorithm such as stochastic gradient descent. These procedures mirror two methods of computing gradients for recurrent neural networks and have different trade-offs in terms of running time and space requirements. Our formulation of the reverse-mode procedure is linked to previous work by Maclaurin et al. [2015] but does not require reversible dynamics. The forward-mode procedure is suitable for real-time hyperparameter updates, which may significantly speed up hyperparameter optimization on large datasets. We present experiments on data cleaning and on learning task interactions. We also present one large-scale experiment where the use of previous gradient-based methods would be prohibitive.

Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal parameters. Examples of such parameters include individual regression coefficients, average treatment effects, average lifts, and demand or supply elasticities. In fact, estimates of such causal parameters obtained via naively plugging ML estimators into estimating equations for such parameters can behave very poorly due to the regularization bias. Fortunately, this regularization bias can be removed by solving auxiliary prediction problems via ML tools. Specifically, we can form an orthogonal score for the target low-dimensional parameter by combining auxiliary and main ML predictions. The score is then used to build a de-biased estimator of the target parameter which typically will converge at the fastest possible 1/root(n) rate and be approximately unbiased and normal, and from which valid confidence intervals for these parameters of interest may be constructed. The resulting method thus could be called a "double ML" method because it relies on estimating primary and auxiliary predictive models. In order to avoid overfitting, our construction also makes use of the K-fold sample splitting, which we call cross-fitting. This allows us to use a very broad set of ML predictive methods in solving the auxiliary and main prediction problems, such as random forest, lasso, ridge, deep neural nets, boosted trees, as well as various hybrids and aggregators of these methods.