Statistical Inference for Feature Selection after Optimal Transport-based Domain Adaptation

Feature Selection (FS) under domain adaptation (DA) is a critical task in machine learning, especially when dealing with limited target data. However, existing methods lack the capability to guarantee the reliability of FS under DA. In this paper, we introduce a novel statistical method to statistically test FS reliability under DA, named SFS-DA (statistical FS-DA). The key strength of SFS-DA lies in its ability to control the false positive rate (FPR) below a pre-specified level $\alpha$ (e.g., 0.05) while maximizing the true positive rate. Compared to the literature on statistical FS, SFS-DA presents a unique challenge in addressing the effect of DA to ensure the validity of the inference on FS results. We overcome this challenge by leveraging the Selective Inference (SI) framework. Specifically, by carefully examining the FS process under DA whose operations can be characterized by linear and quadratic inequalities, we prove that achieving FPR control in SFS-DA is indeed possible. Furthermore, we enhance the true detection rate by introducing a more strategic approach. Experiments conducted on both synthetic and real-world datasets robustly support our theoretical results, showcasing the superior performance of the proposed SFS-DA method.

Controllable RANSAC-based Anomaly Detection via Hypothesis Testing

Detecting the presence of anomalies in regression models is a crucial task in machine learning, as anomalies can significantly impact the accuracy and reliability of predictions. Random Sample Consensus (RANSAC) is one of the most popular robust regression methods for addressing this challenge. However, this method lacks the capability to guarantee the reliability of the anomaly detection (AD) results. In this paper, we propose a novel statistical method for testing the AD results obtained by RANSAC, named CTRL-RANSAC (controllable RANSAC). The key strength of the proposed method lies in its ability to control the probability of misidentifying anomalies below a pre-specified level $\alpha$ (e.g., $\alpha = 0.05$). By examining the selection strategy of RANSAC and leveraging the Selective Inference (SI) framework, we prove that achieving controllable RANSAC is indeed feasible. Furthermore, we introduce a more strategic and computationally efficient approach to enhance the true detection rate and overall performance of the CTRL-RANSAC. Experiments conducted on synthetic and real-world datasets robustly support our theoretical results, showcasing the superior performance of the proposed method.

Statistical Test for Generated Hypotheses by Diffusion Models

The enhanced performance of AI has accelerated its integration into scientific research. In particular, the use of generative AI to create scientific hypotheses is promising and is increasingly being applied across various fields. However, when employing AI-generated hypotheses for critical decisions, such as medical diagnoses, verifying their reliability is crucial. In this study, we consider a medical diagnostic task using generated images by diffusion models, and propose a statistical test to quantify its reliability. The basic idea behind the proposed statistical test is to employ a selective inference framework, where we consider a statistical test conditional on the fact that the generated images are produced by a trained diffusion model. Using the proposed method, the statistical reliability of medical image diagnostic results can be quantified in the form of a p-value, allowing for decision-making with a controlled error rate. We show the theoretical validity of the proposed statistical test and its effectiveness through numerical experiments on synthetic and brain image datasets.

Statistical Test for Anomaly Detections by Variational Auto-Encoders

In this study, we consider the reliability assessment of anomaly detection (AD) using Variational Autoencoder (VAE). Over the last decade, VAE-based AD has been actively studied in various perspective, from method development to applied research. However, when the results of ADs are used in high-stakes decision-making, such as in medical diagnosis, it is necessary to ensure the reliability of the detected anomalies. In this study, we propose the VAE-AD Test as a method for quantifying the statistical reliability of VAE-based AD within the framework of statistical testing. Using the VAE-AD Test, the reliability of the anomaly regions detected by a VAE can be quantified in the form of p-values. This means that if an anomaly is declared when the p-value is below a certain threshold, it is possible to control the probability of false detection to a desired level. Since the VAE-AD Test is constructed based on a new statistical inference framework called selective inference, its validity is theoretically guaranteed in finite samples. To demonstrate the validity and effectiveness of the proposed VAE-AD Test, numerical experiments on artificial data and applications to brain image analysis are conducted.

Statistical Test for Attention Map in Vision Transformer

The Vision Transformer (ViT) demonstrates exceptional performance in various computer vision tasks. Attention is crucial for ViT to capture complex wide-ranging relationships among image patches, allowing the model to weigh the importance of image patches and aiding our understanding of the decision-making process. However, when utilizing the attention of ViT as evidence in high-stakes decision-making tasks such as medical diagnostics, a challenge arises due to the potential of attention mechanisms erroneously focusing on irrelevant regions. In this study, we propose a statistical test for ViT's attentions, enabling us to use the attentions as reliable quantitative evidence indicators for ViT's decision-making with a rigorously controlled error rate. Using the framework called selective inference, we quantify the statistical significance of attentions in the form of p-values, which enables the theoretically grounded quantification of the false positive detection probability of attentions. We demonstrate the validity and the effectiveness of the proposed method through numerical experiments and applications to brain image diagnoses.

Selective Inference for Changepoint detection by Recurrent Neural Network

In this study, we investigate the quantification of the statistical reliability of detected change points (CPs) in time series using a Recurrent Neural Network (RNN). Thanks to its flexibility, RNN holds the potential to effectively identify CPs in time series characterized by complex dynamics. However, there is an increased risk of erroneously detecting random noise fluctuations as CPs. The primary goal of this study is to rigorously control the risk of false detections by providing theoretically valid p-values to the CPs detected by RNN. To achieve this, we introduce a novel method based on the framework of Selective Inference (SI). SI enables valid inferences by conditioning on the event of hypothesis selection, thus mitigating selection bias. In this study, we apply SI framework to RNN-based CP detection, where characterizing the complex process of RNN selecting CPs is our main technical challenge. We demonstrate the validity and effectiveness of the proposed method through artificial and real data experiments.

CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inference

We propose a novel statistical method for testing the results of anomaly detection (AD) under domain adaptation (DA), which we call CAD-DA -- controllable AD under DA. The distinct advantage of the CAD-DA lies in its ability to control the probability of misidentifying anomalies under a pre-specified level $\alpha$ (e.g., 0.05). The challenge within this DA setting is the necessity to account for the influence of DA to ensure the validity of the inference results. Our solution to this challenge leverages the concept of conditional Selective Inference to handle the impact of DA. To our knowledge, this is the first work capable of conducting a valid statistical inference within the context of DA. We evaluate the performance of the CAD-DA method on both synthetic and real-world datasets.

Bounded P-values in Parametric Programming-based Selective Inference

Selective inference (SI) has been actively studied as a promising framework for statistical hypothesis testing for data-driven hypotheses. The basic idea of SI is to make inferences conditional on an event that a hypothesis is selected. In order to perform SI, this event must be characterized in a traceable form. When selection event is too difficult to characterize, additional conditions are introduced for tractability. This additional conditions often causes the loss of power, and this issue is referred to as over-conditioning. Parametric programming-based SI (PP-based SI) has been proposed as one way to address the over-conditioning issue. The main problem of PP-based SI is its high computational cost due to the need to exhaustively explore the data space. In this study, we introduce a procedure to reduce the computational cost while guaranteeing the desired precision, by proposing a method to compute the upper and lower bounds of p-values. We also proposed three types of search strategies that efficiently improve these bounds. We demonstrate the effectiveness of the proposed method in hypothesis testing problems for feature selection in linear models and attention region identification in deep neural networks.

Valid P-Value for Deep Learning-Driven Salient Region

Various saliency map methods have been proposed to interpret and explain predictions of deep learning models. Saliency maps allow us to interpret which parts of the input signals have a strong influence on the prediction results. However, since a saliency map is obtained by complex computations in deep learning models, it is often difficult to know how reliable the saliency map itself is. In this study, we propose a method to quantify the reliability of a salient region in the form of p-values. Our idea is to consider a salient region as a selected hypothesis by the trained deep learning model and employ the selective inference framework. The proposed method can provably control the probability of false positive detections of salient regions. We demonstrate the validity of the proposed method through numerical examples in synthetic and real datasets. Furthermore, we develop a Keras-based framework for conducting the proposed selective inference for a wide class of CNNs without additional implementation cost.

Exact Statistical Inference for Time Series Similarity using Dynamic Time Warping by Selective Inference

In this paper, we study statistical inference on the similarity/distance between two time-series under uncertain environment by considering a statistical hypothesis test on the distance obtained from Dynamic Time Warping (DTW) algorithm. The sampling distribution of the DTW distance is too complicated to derive because it is obtained based on the solution of a complicated algorithm. To circumvent this difficulty, we propose to employ a conditional sampling distribution for the inference, which enables us to derive an exact (non-asymptotic) inference method on the DTW distance. Besides, we also develop a novel computational method to compute the conditional sampling distribution. To our knowledge, this is the first method that can provide valid $p$-value to quantify the statistical significance of the DTW distance, which is helpful for high-stake decision making. We evaluate the performance of the proposed inference method on both synthetic and real-world datasets.