Interactive data exploration (IDE) is an effective way of comprehending big data, whose volume and complexity are beyond human abilities. The main goal of IDE is to discover user interest regions from a database through multi-rounds of user labelling. Existing IDEs adopt active-learning framework, where users iteratively discriminate or label the interestingness of selected tuples. The process of data exploration can be viewed as the process of training a classifier, which determines whether a database tuple is interesting to a user. An efficient exploration thus takes very few iterations of user labelling to reach the data region of interest. In this work, we consider the data exploration as the process of few-shot learning, where the classifier is learned with only a few training examples, or exploration iterations. To this end, we propose a learning-to-explore framework, based on meta-learning, which learns how to learn a classifier with automatically generated meta-tasks, so that the exploration process can be much shortened. Extensive experiments on real datasets show that our proposal outperforms existing explore-by-example solutions in terms of accuracy and efficiency.

When comparing approximate Gaussian process (GP) models, it can be helpful to be able to generate data from any GP. If we are interested in how approximate methods perform at scale, we may wish to generate very large synthetic datasets to evaluate them. Na\"{i}vely doing so would cost \(\mathcal{O}(n^3)\) flops and \(\mathcal{O}(n^2)\) memory to generate a size \(n\) sample. We demonstrate how to scale such data generation to large \(n\) whilst still providing guarantees that, with high probability, the sample is indistinguishable from a sample from the desired GP.

Clustering is one of the most studied problems in machine learning with various applications in analyzing and visualizing large datasets. There are various models and technique to obtain a partition of elements, such that elements belonging to different partitions are dissimilar to each other and the elements in the same partition are very similar to each other. The problem of correlation clustering, introduced in [1], is known to be an NP-hard problem for the disagree minimization. Therefore, several different approximation solutions based on its IP formulation exist in the literature. Recently, the idea of a 2-approximation algorithm in [1] is extended in [4] for constructing a O (1)-approximation algorithm. The experiments in [4] show acceptable performance for this algorithm in practice, although its theoretical guarantee can be too high, e.g. 1 442 for β = λ =

Inspired by the success of contrastive learning (CL) in computer vision and natural language processing, graph contrastive learning (GCL) has been developed to learn discriminative node representations on graph datasets. However, the development of GCL on Heterogeneous Information Networks (HINs) is still in the infant stage. For example, it is unclear how to augment the HINs without substantially altering the underlying semantics, and how to design the contrastive objective to fully capture the rich semantics. Moreover, early investigations demonstrate that CL suffers from sampling bias, whereas conventional debiasing techniques are empirically shown to be inadequate for GCL. How to mitigate the sampling bias for heterogeneous GCL is another important problem. To address the aforementioned challenges, we propose a novel Heterogeneous Graph Contrastive Multi-view Learning (HGCML) model. In particular, we use metapaths as the augmentation to generate multiple subgraphs as multi-views, and propose a contrastive objective to maximize the mutual information between any pairs of metapath-induced views. To alleviate the sampling bias, we further propose a positive sampling strategy to explicitly select positives for each node via jointly considering semantic and structural information preserved on each metapath view. Extensive experiments demonstrate HGCML consistently outperforms state-of-the-art baselines on five real-world benchmark datasets.

Weight decay, also known as L2 regularization, is a technique used in machine learning to prevent overfitting by adding a penalty term to the objective function that is being optimized. The goal of weight decay is to reduce the complexity of the model by limiting the size of the weights, which can help to prevent overfitting and improve the generalization ability of the model. Weight decay is typically implemented by adding a term to the objective function that is proportional to the sum of the squares of the weights. The strength of the weight decay penalty is controlled by a hyperparameter called the decay rate or regularization strength, which determines the amount of weight decay applied to the model. For example, let's say we are training a linear regression model to predict the price of a house based on the number of bedrooms and the square footage.

Mango is a python library to find the optimal hyperparameters for machine learning classifiers. Mango is straightforward to use. Following example minimizes the quadratic function whose input is an integer between -10 and 10. Note that best parameters may be different but accuracy should be 0.9315. More examples are available in the examples directory (Facebook's Prophet, XGBoost, SVM).

Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional scalings. Here, we express this symmetry in terms of a (non-compact) group action, and we employ dimensional analysis and ideas from equivariant machine learning to provide a methodology for exactly units-equivariant machine learning: For any given learning task, we first construct a dimensionless version of its inputs using classic results from dimensional analysis, and then perform inference in the dimensionless space. Our approach can be used to impose units equivariance across a broad range of machine learning methods which are equivariant to rotations and other groups. We discuss the in-sample and out-of-sample prediction accuracy gains one can obtain in contexts like symbolic regression and emulation, where symmetry is important. We illustrate our approach with simple numerical examples involving dynamical systems in physics and ecology.

This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its asymptotic behavior in a non-asymptotic fashion. An important feature of our bound is that its dimension dependency is captured by the effective dimension $\unicode{x2013}$ the trace of the limiting sandwich covariance $\unicode{x2013}$ which can be much smaller than the parameter dimension in some regimes. We then illustrate how the bound can be used to obtain a confidence set whose shape is adapted to the optimization landscape induced by the loss function. Unlike previous works that rely heavily on the strong convexity of the loss function, we only assume the Hessian is lower bounded at optimum and allow it to gradually becomes degenerate. This property is formalized by the notion of generalized self-concordance which originated from convex optimization. Moreover, we demonstrate how the effective dimension can be estimated from data and characterize its estimation accuracy. We apply our results to maximum likelihood estimation with generalized linear models, score matching with exponential families, and hypothesis testing with Rao's score test.

Resilience denotes the capacity of a system to withstand shocks and its ability to recover from them. We develop a framework to quantify the resilience of highly volatile, non-equilibrium social organizations, such as collectives or collaborating teams. It consists of four steps: (i) \emph{delimitation}, i.e., narrowing down the target systems, (ii) \emph{conceptualization}, .e., identifying how to approach social organizations, (iii) formal \emph{representation} using a combination of agent-based and network models, (iv) \emph{operationalization}, i.e. specifying measures and demonstrating how they enter the calculation of resilience. Our framework quantifies two dimensions of resilience, the \emph{robustness} of social organizations and their \emph{adaptivity}, and combines them in a novel resilience measure. It allows monitoring resilience instantaneously using longitudinal data instead of an ex-post evaluation.

Exposure to crime and violence can harm individuals' quality of life and the economic growth of communities. In light of the rapid development in machine learning, there is a rise in the need to explore automated solutions to prevent crimes. With the increasing availability of both fine-grained urban and public service data, there is a recent surge in fusing such cross-domain information to facilitate crime prediction. By capturing the information about social structure, environment, and crime trends, existing machine learning predictive models have explored the dynamic crime patterns from different views. However, these approaches mostly convert such multi-source knowledge into implicit and latent representations (e.g., learned embeddings of districts), making it still a challenge to investigate the impacts of explicit factors for the occurrences of crimes behind the scenes. In this paper, we present a Spatial-Temporal Metapath guided Explainable Crime prediction (STMEC) framework to capture dynamic patterns of crime behaviours and explicitly characterize how the environmental and social factors mutually interact to produce the forecasts. Extensive experiments show the superiority of STMEC compared with other advanced spatiotemporal models, especially in predicting felonies (e.g., robberies and assaults with dangerous weapons).