SHAP also suffers under high variance in the Feature-2 attribution for extreme values.

Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been proposed for this task which make fewer assumptions on the distributions than traditional parametric approach. However, none of the existing kernel statistics has provided a computationally efficient way to characterize the extremal behavior of the statistic. Such characterization is crucial for setting the detection threshold, to control the significance level in the offline case as well as the average run length in the online case. In this paper we propose two related computationally efficient M -statistics for kernel-based change-point detection when the amount of background data is large. A novel theoretical result of the paper is the characterization of the tail probability of these statistics using a new technique based on change-of-measure. Such characterization provides us accurate detection thresholds for both offline and online cases in computationally efficient manner, without the need to resort to the more expensive simulations such as bootstrapping. We show that our methods perform well in both synthetic and real world data.

It is important to also demonstrate the robustness of the proposed algorithm on data relative to the naive model.

In many natural settings, the analysis goal is not to characterize a single data set in isolation, but rather to understand the difference between one set of observations and another. For example, given a background corpus of news articles together with writings of a particular author, one may want a topic model that explains word patterns and themes specific to the author. Another example comes from genomics, in which biological signals may be collected from different regions of a genome, and one wants a model that captures the differential statistics observed in these regions. This paper formalizes this notion of contrastive learning for mixture models, and develops spectral algorithms for inferring mixture components specific to a foreground data set when contrasted with a background data set. The method builds on recent moment-based estimators and tensor decompositions for latent variable models, and has the intuitive feature of using background data statistics to appropriately modify moments estimated from foreground data.

Imitation Learning from Observation (IfO) offers a powerful way to learn behaviors at large-scale: Unlike behavior cloning or offline reinforcement learning, IfO can leverage action-free demonstrations and thus circumvents the need for costly action-labeled demonstrations or reward functions. However, current IfO research focuses on idealized scenarios with mostly bimodal-quality data distributions, restricting the meaningfulness of the results. In contrast, this paper investigates more nuanced distributions and introduces a method to learn from such data, moving closer to a paradigm in which imitation learning can be performed iteratively via self-improvement. Our method adapts RL-based imitation learning to action-free demonstrations, using a value function to transfer information between expert and non-expert data. Through comprehensive evaluation, we delineate the relation between different data distributions and the applicability of algorithms and highlight the limitations of established methods. Our findings provide valuable insights for developing more robust and practical IfO techniques on a path to scalable behaviour learning.

In many natural settings, the analysis goal is not to characterize a single data set in isolation, but rather to understand the difference between one set of observations and another. For example, given a background corpus of news articles together with writings of a particular author, one may want a topic model that explains word patterns and themes specific to the author. Another example comes from genomics, in which biological signals may be collected from different regions of a genome, and one wants a model that captures the differential statistics observed in these regions. This paper formalizes this notion of contrastive learning for mixture models, and develops spectral algorithms for inferring mixture components specific to a foreground data set when contrasted with a background data set. The method builds on recent moment-based estimators and tensor decompositions for latent variable models, and has the intuitive feature of using background data statistics to appropriately modify moments estimated from foreground data. A key advantage of the method is that the background data need only be coarsely modeled, which is important when the background is too complex, noisy, or not of interest. The method is demonstrated on applications in contrastive topic modeling and genomic sequence analysis.

Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been proposed for this task which make fewer assumptions on the distributions than traditional parametric approach. However, none of the existing kernel statistics has provided a computationally efficient way to characterize the extremal behavior of the statistic. Such characterization is crucial for setting the detection threshold, to control the significance level in the offline case as well as the average run length in the online case. In this paper we propose two related computationally efficient M-statistics for kernel-based change-point detection when the amount of background data is large. A novel theoretical result of the paper is the characterization of the tail probability of these statistics using a new technique based on change-ofmeasure. Such characterization provides us accurate detection thresholds for both offline and online cases in computationally efficient manner, without the need to resort to the more expensive simulations such as bootstrapping. We show that our methods perform well in both synthetic and real world data.

Deep Generative Models (DGMs) are versatile tools for learning data representations while adequately incorporating domain knowledge such as the specification of conditional probability distributions. Recently proposed DGMs tackle the important task of comparing data sets from different sources. One such example is the setting of contrastive analysis that focuses on describing patterns that are enriched in a target data set compared to a background data set. The practical deployment of those models often assumes that DGMs naturally infer interpretable and modular latent representations, which is known to be an issue in practice. Consequently, existing methods often rely on ad-hoc regularization schemes, although without any theoretical grounding. Here, we propose a theory of identifiability for comparative DGMs by extending recent advances in the field of non-linear independent component analysis. We show that, while these models lack identifiability across a general class of mixing functions, they surprisingly become identifiable when the mixing function is piece-wise affine (e.g., parameterized by a ReLU neural network). We also investigate the impact of model misspecification, and empirically show that previously proposed regularization techniques for fitting comparative DGMs help with identifiability when the number of latent variables is not known in advance. Finally, we introduce a novel methodology for fitting comparative DGMs that improves the treatment of multiple data sources via multi-objective optimization and that helps adjust the hyperparameter for the regularization in an interpretable manner, using constrained optimization. We empirically validate our theory and new methodology using simulated data as well as a recent data set of genetic perturbations in cells profiled via single-cell RNA sequencing.

N-ary facts composed of a primary triple (head entity, relation, tail entity) and an arbitrary number of auxiliary attribute-value pairs, are prevalent in real-world knowledge graphs (KGs). Link prediction on n-ary facts is to predict a missing element in an n-ary fact. This helps populate and enrich KGs and further promotes numerous downstream applications. Previous studies usually require a substantial amount of high-quality data to understand the elements in n-ary facts. However, these studies overlook few-shot relations, which have limited labeled instances, yet are common in real-world scenarios. Thus, this paper introduces a new task, few-shot link prediction on n-ary facts. It aims to predict a missing entity in an n-ary fact with limited labeled instances. We further propose a model for Few-shot Link prEdict on N-ary facts, thus called FLEN, which consists of three modules: the relation learning, support-specific adjusting, and query inference modules. FLEN captures relation meta information from limited instances to predict a missing entity in a query instance. To validate the effectiveness of FLEN, we construct three datasets based on existing benchmark data. Our experimental results show that FLEN significantly outperforms existing related models in both few-shot link prediction on n-ary facts and binary facts.