Using a single train-test split gives you a single snapshot of the performance of a machine learning model or algorithm. It's like evaluating a football team (American or otherwise) based on a single game. If you really want to know how well a team performs in general, you're going to want more than just this snapshot. Likewise, we shouldn't evaluate our algorithms on a single random split. I bring you k-fold cross validation.

We study how well Local Causal Discovery (LCD), a simple and efficient constraint-based method for causal discovery, is able to predict causal effects in large-scale gene expression data. We construct practical estimators specific to the high-dimensional regime. Inspired by ICP, we use an optional preselection method and two different statistical tests. Empirically, the resulting LCD estimator is seen to closely approach the accuracy of ICP, the state-of-the-art method, while it is algorithmically simpler and computationally more efficient.

We study the following three fundamental problems about ridge regression: (1) what is the structure of the estimator? (2) how to correctly use cross-validation to choose the regularization parameter? and (3) how to accelerate computation without losing too much accuracy? We consider the three problems in a unified large-data linear model. We give a precise representation of ridge regression as a covariance matrix-dependent linear combination of the true parameter and the noise. We study the bias of $K$-fold cross-validation for choosing the regularization parameter, and propose a simple bias-correction. We analyze the accuracy of primal and dual sketching for ridge regression, showing they are surprisingly accurate. Our results are illustrated by simulations and by analyzing empirical data.

Deep generative models are generally categorized into explicit models and implicit models. The former defines an explicit density form, whose normalizing constant is often unknown; while the latter, including generative adversarial networks (GANs), generates samples without explicitly defining a density function. In spite of substantial recent advances demonstrating the power of the two classes of generative models in many applications, both of them, when used alone, suffer from respective limitations and drawbacks. To mitigate these issues, we propose Stein Bridging, a novel joint training framework that connects an explicit density estimator and an implicit sample generator with Stein discrepancy. We show that the Stein Bridge induces new regularization schemes for both explicit and implicit models. Convergence analysis and extensive experiments demonstrate that the Stein Bridging i) improves the stability and sample quality of the GAN training, and ii) facilitates the density estimator to seek more modes in data and alleviate the mode-collapse issue. Additionally, we discuss several applications of Stein Bridging and useful tricks in practical implementation used in our experiments.

--Machine learning models are widely adopted in scenarios that directly affect people. The development of software systems based on these models raises societal and legal concerns, as their decisions may lead to the unfair treatment of individuals based on attributes like race or gender . Data preparation is key in any machine learning pipeline, but its effect on fairness is yet to be studied in detail. In this paper, we evaluate how the fairness and effectiveness of the learned models are affected by the removal of the sensitive attribute, the encoding of the categorical attributes, and instance selection methods (including cross-validators and random undersampling). We used the Adult Income and the German Credit Data datasets, which are widely studied and known to have fairness concerns. We applied each data preparation technique individually to analyse the difference in predictive performance and fairness, using statistical parity difference, disparate impact, and the normalised prejudice index. The results show that fairness is affected by transformations made to the training data, particularly in imbalanced datasets. Removing the sensitive attribute is insufficient to eliminate all the unfairness in the predictions, as expected, but it is key to achieve fairer models. Additionally, the standard random undersampling with respect to the true labels is sometimes more prejudicial than performing no random undersampling. Software systems based on machine learning (ML) are being used at an increasingly higher rate and on a multitude of scenarios that have a significant impact on people's lives. Their ubiquity raises several legal and societal concerns, as decisions based on the output of ML models may introduce or perpetuate historical bias against some individuals, based on their intrinsic characteristics, such as race, gender or age. The use of automated decision-making systems is often appealing due to the gains associated with it, and might even be perceived as a step towards the eradication of personal bias from the process. Nevertheless, many are the risks associated with a careless adoption of decisions supported by these systems. In this context, fairness emerges as a key property in terms of the reliability and trustworthiness of software systems based on ML. These receive nowadays increased attention from regulatory institutions, with the recently approved European Union General Data Protection Regulation (GDPR) demanding organisations to handle personal data in a privacy-preserving, fair and transparent manner [1].

Evaluation metrics are used to measure the quality of the statistical or machine learning model. Evaluating machine learning models or algorithms is essential for any project. There are many different types of evaluation metrics available to test a model. These include classification accuracy, logarithmic loss, confusion matrix, and others. Classification accuracy is the ratio of the number of correct predictions to the total number of input samples, which is usually what we refer to when we use the term accuracy.

The number of shiny models out there can be overwhelming, which means a lot of times people fall back on a few they trust the most and use them on all new problems. This can lead to sub-optimal results. Today we're going to learn how to quickly and efficiently narrow down the space of available models to find those that are most likely to perform best on your problem type. We'll also see how we can keep track of our models' performances using Weights and Biases and compare them. You can find the accompanying code here.

In point-based sensing systems such as coordinate measuring machines (CMM) and laser ultrasonics where complete sensing is impractical due to the high sensing time and cost, adaptive sensing through a systematic exploration is vital for online inspection and anomaly quantification. Most of the existing sequential sampling methodologies focus on reducing the overall fitting error for the entire sampling space. However, in many anomaly quantification applications, the main goal is to estimate sparse anomalous regions in the pixel-level accurately. In this paper, we develop a novel framework named Adaptive Kernelized Maximum-Minimum Distance AKM$^2$D to speed up the inspection and anomaly detection process through an intelligent sequential sampling scheme integrated with fast estimation and detection. The proposed method balances the sampling efforts between the space-filling sampling (exploration) and focused sampling near the anomalous region (exploitation). The proposed methodology is validated by conducting simulations and a case study of anomaly detection in composite sheets using a guided wave test.

Because of high dimensionality, correlation among covariates, and noise contained in data, dimension reduction (DR) techniques are often employed to the application of machine learning algorithms. Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and their kernel variants (KPCA, KLDA) are among the most popular DR methods. Recently, Supervised Kernel Principal Component Analysis (SKPCA) has been shown as another successful alternative. In this paper, brief reviews of these popular techniques are presented first. We then conduct a comparative performance study based on three simulated datasets, after which the performance of the techniques are evaluated through application to a pattern recognition problem in face image analysis. The gender classification problem is considered on MORPH-II and FG-NET, two popular longitudinal face aging databases. Several feature extraction methods are used, including biologically-inspired features (BIF), local binary patterns (LBP), histogram of oriented gradients (HOG), and the Active Appearance Model (AAM). After applications of DR methods, a linear support vector machine (SVM) is deployed with gender classification accuracy rates exceeding 95% on MORPH-II, competitive with benchmark results. A parallel computational approach is also proposed, attaining faster processing speeds and similar recognition rates on MORPH-II. Our computational approach can be applied to practical gender classification systems and generalized to other face analysis tasks, such as race classification and age prediction.

Computing expected predictions has many interesting applications in areas such as fairness, handling missing values, and data analysis. Unfortunately, computing expectations of a discriminative model with respect to a probability distribution defined by an arbitrary generative model has been proven to be hard in general. In fact, the task is intractable even for simple models such as logistic regression and a naive Bayes distribution. In this paper, we identify a pair of generative and discriminative models that enables tractable computation of expectations of the latter with respect to the former, as well as moments of any order, in case of regression. Specifically, we consider expressive probabilistic circuits with certain structural constraints that support tractable probabilistic inference. Moreover, we exploit the tractable computation of high-order moments to derive an algorithm to approximate the expectations, for classification scenarios in which exact computations are intractable. We evaluate the effectiveness of our exact and approximate algorithms in handling missing data during prediction time where they prove to be competitive to standard imputation techniques on a variety of datasets. Finally, we illustrate how expected prediction framework can be used to reason about the behaviour of discriminative models.