Metric Multidimensional scaling (MDS) is a classical method for generating meaningful (non-linear) low-dimensional embeddings of high-dimensional data. MDS has a long history in the statistics, machine learning, and graph drawing communities. In particular, the Kamada-Kawai force-directed graph drawing method is equivalent to MDS and is one of the most popular ways in practice to embed graphs into low dimensions. Despite its ubiquity, our theoretical understanding of MDS remains limited as its objective function is highly non-convex. In this paper, we prove that minimizing the Kamada-Kawai objective is NP-hard and give a provable approximation algorithm for optimizing it, which in particular is a PTAS on low-diameter graphs.

Recent \emph{Weak Supervision (WS)} approaches have had widespread success in easing the bottleneck of labeling training data for machine learning by synthesizing labels from multiple potentially noisy supervision sources. However, proper measurement and analysis of these approaches remain a challenge. First, datasets used in existing works are often private and/or custom, limiting standardization. Second, WS datasets with the same name and base data often vary in terms of the labels and weak supervision sources used, a significant "hidden" source of evaluation variance. Finally, WS studies often diverge in terms of the evaluation protocol and ablations used. To address these problems, we introduce a benchmark platform, \benchmark, for a thorough and standardized evaluation of WS approaches. It consists of 22 varied real-world datasets for classification and sequence tagging; a range of real, synthetic, and procedurally-generated weak supervision sources; and a modular, extensible framework for WS evaluation, including implementations for popular WS methods. We use \benchmark to conduct extensive comparisons over more than 100 method variants to demonstrate its efficacy as a benchmark platform. The code is available at \url{https://github.com/JieyuZ2/wrench}.

Pool-based active learning (AL) aims to optimize the annotation process (i.e., labeling) as the acquisition of annotations is often time-consuming and therefore expensive. For this purpose, an AL strategy queries annotations intelligently from annotators to train a high-performance classification model at a low annotation cost. Traditional AL strategies operate in an idealized framework. They assume a single, omniscient annotator who never gets tired and charges uniformly regardless of query difficulty. However, in real-world applications, we often face human annotators, e.g., crowd or in-house workers, who make annotation mistakes and can be reluctant to respond if tired or faced with complex queries. Recently, a wide range of novel AL strategies has been proposed to address these issues. They differ in at least one of the following three central aspects from traditional AL: (1) They explicitly consider (multiple) human annotators whose performances can be affected by various factors, such as missing expertise. (2) They generalize the interaction with human annotators by considering different query and annotation types, such as asking an annotator for feedback on an inferred classification rule. (3) They take more complex cost schemes regarding annotations and misclassifications into account. This survey provides an overview of these AL strategies and refers to them as real-world AL. Therefore, we introduce a general real-world AL strategy as part of a learning cycle and use its elements, e.g., the query and annotator selection algorithm, to categorize about 60 real-world AL strategies. Finally, we outline possible directions for future research in the field of AL.

This paper considers binary and multilabel classification problems in a setting where labels are missing independently and with a known rate. Missing labels are a ubiquitous phenomenon in extreme multi-label classification (XMC) tasks, such as matching Wikipedia articles to a small subset out of the hundreds of thousands of possible tags, where no human annotator can possibly check the validity of all the negative samples. For this reason, propensity-scored precision -- an unbiased estimate for precision-at-k under a known noise model -- has become one of the standard metrics in XMC. Few methods take this problem into account already during the training phase, and all are limited to loss functions that can be decomposed into a sum of contributions from each individual label. A typical approach to training is to reduce the multilabel problem into a series of binary or multiclass problems, and it has been shown that if the surrogate task should be consistent for optimizing recall, the resulting loss function is not decomposable over labels. Therefore, this paper derives the unique unbiased estimators for the different multilabel reductions, including the non-decomposable ones. These estimators suffer from increased variance and may lead to ill-posed optimization problems, which we address by switching to convex upper-bounds. The theoretical considerations are further supplemented by an experimental study showing that the switch to unbiased estimators significantly alters the bias-variance trade-off and may thus require stronger regularization, which in some cases can negate the benefits of unbiased estimation.

There are a variety of settings where vague prior information may be available on the importance of predictors in high-dimensional regression settings. Examples include ordering on the variables offered by their empirical variances (which is typically discarded through standardisation), the lag of predictors when fitting autoregressive models in time series settings, or the level of missingness of the variables. Whilst such orderings may not match the true importance of variables, we argue that there is little to be lost, and potentially much to be gained, by using them. We propose a simple scheme involving fitting a sequence of models indicated by the ordering. We show that the computational cost for fitting all models when ridge regression is used is no more than for a single fit of ridge regression, and describe a strategy for Lasso regression that makes use of previous fits to greatly speed up fitting the entire sequence of models. We propose to select a final estimator by cross-validation and provide a general result on the quality of the best performing estimator on a test set selected from among a number $M$ of competing estimators in a high-dimensional linear regression setting. Our result requires no sparsity assumptions and shows that only a $\log M$ price is incurred compared to the unknown best estimator. We demonstrate the effectiveness of our approach when applied to missing or corrupted data, and time series settings. An R package is available on github.

There are various cluster validity measures used for evaluating clustering results. One of the main objective of using these measures is to seek the optimal unknown number of clusters. Some measures work well for clusters with different densities, sizes and shapes. Yet, one of the weakness that those validity measures share is that they sometimes provide only one clear optimal number of clusters. That number is actually unknown and there might be more than one potential sub-optimal options that a user may wish to choose based on different applications. We develop two new cluster validity indices based on a correlation between an actual distance between a pair of data points and a centroid distance of clusters that the two points locate in. Our proposed indices constantly yield several peaks at different numbers of clusters which overcome the weakness previously stated. Furthermore, the introduced correlation can also be used for evaluating the quality of a selected clustering result. Several experiments in different scenarios including the well-known iris data set and a real-world marketing application have been conducted in order to compare the proposed validity indices with several well-known ones.

This article considers the popular MCMC method of unadjusted Langevin Monte Carlo (LMC) and provides a non-asymptotic analysis of its sampling error in 2-Wasserstein distance. The proof is based on a mean-square analysis framework refined from Li et al. (2019), which works for a large class of sampling algorithms based on discretizations of contractive SDEs. We establish an $\tilde{O}(\sqrt{d}/\epsilon)$ mixing time bound for LMC, without warm start, under the common log-smooth and log-strongly-convex conditions, plus a growth condition on the 3rd-order derivative of the potential of target measures. This bound improves the best previously known $\tilde{O}(d/\epsilon)$ result and is optimal (in terms of order) in both dimension $d$ and accuracy tolerance $\epsilon$ for target measures satisfying the aforementioned assumptions. Our theoretical analysis is further validated by numerical experiments.

This code pattern describes a way to gain insights by using Watson OpenScale and a SageMaker machine learning model. It explains how to create a logistic regression model using Amazon SageMaker with data from the UC Irvine machine learning database. The pattern uses Watson OpenScale to bind the machine learning model deployed in the AWS cloud, create a subscription, and perform payload and feedback logging. With Watson OpenScale, you can monitor model quality and log payloads, regardless of where the model is hosted. This code pattern uses the example of an Amazon Web Service (AWS) SageMaker model, which demonstrates the independent and open nature of Watson OpenScale.

In this chapter the programs fit_func_miso.py and fit_func_mimo.py are presented and they are technically wrappers of the class XGBRFRegressor of the XGBoost library and which purpose is to allow the use of the regression of the underlying regressor to fit functions without having to write code but only acting on the command line. In fact through the argument --xgbparams the user passes a series of hyper-parameters to adjust the behavior of the underlying XGBoost regressor algorithm and others to configure its learning phase. In addition to the parameters of the underlying regressor the two programs support their own arguments to allow the user to pass the training dataset and optionally the validation dataset, on which file to save the trained model, the metrics to calculate during the training, constraints for regularization (e.g. The program fit_func_miso.py, as well as the underlying XGBoost regressor, is of type M.I.S.O., i.e. Multiple Input Single Output: it is designed to fit a function of the form $f \colon \rm I\!R n \to \rm I\!R$ where the number of independent variables is arbitrarily large while the output dependent variable is only one.

Power transformer is an essential component for the stable and reliable operation of electrical power grid. The traditional diagnostic methods based on dissolved gas analysis (DGA) have been used to identify the power transformer faults. However, the application of these methods is limited due to the low accuracy of fault identification. In this paper, a transformer fault diagnosis system is developed based on the combination of an improved genetic algorithm (IGA) and the XGBoost. In the transformer fault diagnosis system, the improved genetic algorithm is employed to pre-select the input features from the DGA data and optimize the XGBoost classifier. Performance measures such as average unfitness value, likelihood of evolution leap, and likelihood of optimality are used to validate the efficacy of the proposed improved genetic algorithm. The results of simulation experiments show that the improved genetic algorithm can get the optimal solution stably and reliably, and the proposed method improves the average accuracy of transformer fault diagnosis to 99.2\%. Compared to IEC ratios, dual triangle, support vector machine (SVM), and common vector approach (CVA), the diagnostic accuracy of the proposed method is improved by 30.2\%, 47.2\%, 11.2\%, and 3.6\%, respectively. The proposed method can be a potential solution to identify the transformer fault types.