All the existing multi-task local learning methods are defined on homogeneous neighborhood which consists of all data points from only one task. In this paper, different from existing methods, we propose local learning methods for multitask classification and regression problems based on heterogeneous neighborhood which is defined on data points from all tasks. Specifically, we extend the k-nearest-neighbor classifier by formulating the decision function for each data point as a weighted voting among the neighbors from all tasks where the weights are task-specific. By defining a regularizer to enforce the task-specific weight matrix to approach a symmetric one, a regularized objective function is proposed and an efficient coordinate descent method is developed to solve it. For regression problems, we extend the kernel regression to multi-task setting in a similar way to the classification case. Experiments on some toy data and real-world datasets demonstrate the effectiveness of our proposed methods.

The detection of anomalous activity in graphs is a statistical problem that arises in many applications, such as network surveillance, disease outbreak detection, and activity monitoring in social networks. Beyond its wide applicability, graph structured anomaly detection serves as a case study in the difficulty of balancing computational complexity with statistical power. In this work, we develop from first principles the generalized likelihood ratio test for determining if there is a well connected region of activation over the vertices in the graph in Gaussian noise. Because this test is computationally infeasible, we provide a relaxation, called the Lovász extended scan statistic (LESS) that uses submodularity to approximate the intractable generalized likelihood ratio. We demonstrate a connection between LESS and maximum a-posteriori inference in Markov random fields, which provides us with a poly-time algorithm for LESS. Using electrical network theory, we are able to control type 1 error for LESS and prove conditions under which LESS is risk consistent. Finally, we consider specific graph models, the torus, k-nearest neighbor graphs, and ǫ-random graphs. We show that on these graphs our results provide near-optimal performance by matching our results to known lower bounds.

We formulate the problem of metric learning for k nearest neighbor classification as a large margin structured prediction problem, with a latent variable representing the choice of neighbors and the task loss directly corresponding to classification error. We describe an efficient algorithm for exact loss augmented inference, and a fast gradient descent algorithm for learning in this model. The objective drives the metric to establish neighborhood boundaries that benefit the true class labels for the training points. Our approach, reminiscent of gerrymandering (redrawing of political boundaries to provide advantage to certain parties), is more direct in its handling of optimizing classification accuracy than those previously proposed. In experiments on a variety of data sets our method is shown to achieve excellent results compared to current state of the art in metric learning.

We present the first sample compression algorithm for nearest neighbors with nontrivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our bound is nearly optimal. Our result yields new insight into margin-based nearest neighbor classification in metric spaces and allows us to significantly sharpen and simplify existing bounds. Some encouraging empirical results are also presented.

Missing values or data is one popular characteristic of real-world datasets, especially healthcare data. This could be frustrating when using machine learning algorithms on such datasets, simply because most machine learning models perform poorly in the presence of missing values. The aim of this study is to compare the performance of seven imputation techniques, namely Mean imputation, Median Imputation, Last Observation carried Forward (LOCF) imputation, K-Nearest Neighbor (KNN) imputation, Interpolation imputation, Missforest imputation, and Multiple imputation by Chained Equations (MICE), on three healthcare datasets. Some percentage of missing values - 10\%, 15\%, 20\% and 25\% - were introduced into the dataset, and the imputation techniques were employed to impute these missing values. The comparison of their performance was evaluated by using root mean squared error (RMSE) and mean absolute error (MAE). The results show that Missforest imputation performs the best followed by MICE imputation. Additionally, we try to determine whether it is better to perform feature selection before imputation or vice versa by using the following metrics - the recall, precision, f1-score and accuracy. Due to the fact that there are few literature on this and some debate on the subject among researchers, we hope that the results from this experiment will encourage data scientists and researchers to perform imputation first before feature selection when dealing with data containing missing values.

We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires k as the sample size n) into the functional of interest, the estimators we consider fix k and perform a bias correction. This is more efficient computationally, and, as we show in certain cases, statistically, leading to faster convergence rates. Our framework unifies several previous estimators, for most of which ours are the first finite sample guarantees.

The weighted k-nearest neighbors algorithm is one of the most fundamental nonparametric methods in pattern recognition and machine learning. The question of setting the optimal number of neighbors as well as the optimal weights has received much attention throughout the years, nevertheless this problem seems to have remained unsettled. In this paper we offer a simple approach to locally weighted regression/classification, where we make the bias-variance tradeoff explicit. Our formulation enables us to phrase a notion of optimal weights, and to efficiently find these weights as well as the optimal number of neighbors efficiently and adaptively, for each data point whose value we wish to estimate. The applicability of our approach is demonstrated on several datasets, showing superior performance over standard locally weighted methods.

We propose a pool-based non-parametric active learning algorithm for general metric spaces, called MArgin Regularized Metric Active Nearest Neighbor (MARMANN), which outputs a nearest-neighbor classifier. We give prediction error guarantees that depend on the noisy-margin properties of the input sample, and are competitive with those obtained by previously proposed passive learners. We prove that the label complexity of MARMANN is significantly lower than that of any passive learner with similar error guarantees. Our algorithm is based on a generalized sample compression scheme and a new label-efficient active model-selection procedure.

Predictive models in natural language processing (NLP) have evolved from training models from scratch to fine-tuning pre-trained models with labelled data. An extreme form of this fine-tuning involves in-context learning (ICL), where the output of a pre-trained generative model (frozen decoder parameters) is controlled only with variations in the input strings (called instructions or prompts). An important component of ICL is the use of a small number of labelled data instances as examples in the prompt. While existing work uses a static number of examples during inference for each data instance, in this paper we propose a novel methodology of dynamically adapting the number of examples as per the data. This is analogous to the use of a variable-sized neighborhood in k-nearest neighbors (k-NN) classifier. In our proposed workflow of adaptive ICL (AICL), the number of demonstrations to employ during the inference on a particular data instance is predicted by the Softmax posteriors of a classifier. The parameters of this classifier are fitted on the optimal number of examples in ICL required to correctly infer the label of each instance in the training set with the hypothesis that a test instance that is similar to a training instance should use the same (or a closely matching) number of few-shot examples. Our experiments show that our AICL method results in improvement in text classification task on several standard datasets.

Financial institutions and businesses face an ongoing challenge from fraudulent transactions, prompting the need for effective detection methods. Detecting credit card fraud is crucial for identifying and preventing unauthorized transactions.Timely detection of fraud enables investigators to take swift actions to mitigate further losses. However, the investigation process is often time-consuming, limiting the number of alerts that can be thoroughly examined each day. Therefore, the primary objective of a fraud detection model is to provide accurate alerts while minimizing false alarms and missed fraud cases. In this paper, we introduce a state-of-the-art hybrid ensemble (ENS) dependable Machine learning (ML) model that intelligently combines multiple algorithms with proper weighted optimization using Grid search, including Decision Tree (DT), Random Forest (RF), K-Nearest Neighbor (KNN), and Multilayer Perceptron (MLP), to enhance fraud identification. To address the data imbalance issue, we employ the Instant Hardness Threshold (IHT) technique in conjunction with Logistic Regression (LR), surpassing conventional approaches. Our experiments are conducted on a publicly available credit card dataset comprising 284,807 transactions. The proposed model achieves impressive accuracy rates of 99.66%, 99.73%, 98.56%, and 99.79%, and a perfect 100% for the DT, RF, KNN, MLP and ENS models, respectively. The hybrid ensemble model outperforms existing works, establishing a new benchmark for detecting fraudulent transactions in high-frequency scenarios. The results highlight the effectiveness and reliability of our approach, demonstrating superior performance metrics and showcasing its exceptional potential for real-world fraud detection applications.