Reconstruction-based methods have been commonly used for unsupervised anomaly detection, in which a normal image is reconstructed and compared with the given test image to detect and locate anomalies. Recently, diffusion models have shown promising applications for anomaly detection due to their powerful generative ability. However, these models lack strict mathematical support for normal image reconstruction and unexpectedly suffer from low reconstruction quality. To address these issues, this paper proposes a novel and highly-interpretable method named Masked Diffusion Posterior Sampling (MDPS). In MDPS, the problem of normal image reconstruction is mathematically modeled as multiple diffusion posterior sampling for normal images based on the devised masked noisy observation model and the diffusion-based normal image prior under Bayesian framework. Using a metric designed from pixel-level and perceptual-level perspectives, MDPS can effectively compute the difference map between each normal posterior sample and the given test image. Anomaly scores are obtained by averaging all difference maps for multiple posterior samples. Exhaustive experiments on MVTec and BTAD datasets demonstrate that MDPS can achieve state-of-the-art performance in normal image reconstruction quality as well as anomaly detection and localization.
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Due to the complex and dynamic traffic contexts, the interpretability and uncertainty of traffic forecasting have gained increasing attention. Significance testing is a powerful tool in statistics used to determine whether a hypothesis is valid, facilitating the identification of pivotal features that predominantly contribute to the true relationship. However, existing works mainly regard traffic forecasting as a deterministic problem, making it challenging to perform effective significance testing. To fill this gap, we propose to conduct Full Bayesian Significance Testing for Neural Networks in Traffic Forecasting, namely ST-nFBST. A Bayesian neural network is utilized to capture the complicated traffic relationships through an optimization function resolved in the context of aleatoric uncertainty and epistemic uncertainty. Thereupon, ST-nFBST can achieve the significance testing by means of a delicate grad-based evidence value, further capturing the inherent traffic schema for better spatiotemporal modeling. Extensive experiments are conducted on METR-LA and PEMS-BAY to verify the advantages of our method in terms of uncertainty analysis and significance testing, helping the interpretability and promotion of traffic forecasting.
A Consistency and Integration Model with Adaptive Thresholds for Weakly Supervised Object Localization
PDF ↗Weakly Supervised Object Localization (WSOL) is a challenging task, which aims to learn object localization with less costly image-level labels. Existing convolution neural network (CNN) based methods tend to focus on discriminative regions of objects, while transformer-based methods overemphasize deep global features powerful for classification and lack the capability to perceive object details, leading to prediction results far from the object boundary. In this paper, we propose a novel Consistency and Integration Model with Adaptive Thresholds (CIAT) that exploits the spatial-semantic consistency between shallow and deep features to activate more object regions and detects the object regions adaptively in different images. First, we introduce a simple plug-and-play consistency and integration module of shallow-deep features (CISD), which utilizes shallow features efficiently to enhance the entire object perception. Then, we design an online adaptive threshold (OAT) based on Bayesian decision theory, which computes a reasonable segmentation threshold adaptive for the localization map of each image, making the predicted bounding box closer to the ground truth. Extensive experiments on two widely used CUB-200-2011 and ILSVRC datasets verify the effectiveness of our methods.
Explanatory Artificial Intelligence plays a vital role in machine learning, due to its widespread application in decision-making scenarios, e.g., credit lending. Counterfactual Explanation (CFE) is a new kind of explanatory method that involves asking “what if ”, i.e. what would have happened if model inputs slightly change. To answer the question, Counterfactual Explanation aims at finding a minimum perturbation in model inputs leading to a different model decision. Compared with model-agnostic approaches, model-specific CFE approaches designed only for specific type of models usually have better performance in finding optimal counterfactual perturbations, owing to access to the inner workings of models. To deal with this dilemma, this work first proposes CMAES-based Counterfactual Explanations (CMACE): an effective model-agnostic counterfactual generating approach based on Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and a warm starting scheme that provides good initialization of the counterfactual's mean and covariance parameters for CMA-ES taking advantage of prior information of training samples. CMACE significantly outperforms another state-of-art (SOTA) model-agnostic approach (Bayesian Counterfactual Generator, BayCon) with various experimental settings. Extensive experiments also demonstrate that CMACE is superior to a SOTA model-specific approach (Flexible Optimizable Counterfactual Explanations for Tree Ensembles, FOCUS) that is designed for tree-based models using gradient-based optimization.
G–LIME: Statistical Learning for Local Interpretations of Deep Neural Networks Using Global Priors (Abstract Reprint)
PDF ↗To explain the prediction result of a Deep Neural Network (DNN) model based on a given sample, LIME [1] and its derivatives have been proposed to approximate the local behavior of the DNN model around the data point via linear surrogates. Though these algorithms interpret the DNN by finding the key features used for classification, the random interpolations used by LIME would perturb the explanation result and cause the instability and inconsistency between repetitions of LIME computations. To tackle this issue, we propose G-LIME that extends the vanilla LIME through high-dimensional Bayesian linear regression using the sparsity and informative global priors. Specifically, with a dataset representing the population of samples (e.g., the training set), G-LIME first pursues the global explanation of the DNN model using the whole dataset. Then, with a new data point, -LIME incorporates an modified estimator of ElasticNet-alike to refine the local explanation result through balancing the distance to the global explanation and the sparsity/feature selection in the explanation. Finally, G-LIME uses Least Angle Regression (LARS) and retrieves the solution path of a modified ElasticNet under varying -regularization, to screen and rank the importance of features [2] as the explanation result. Through extensive experiments on real world tasks, we show that the proposed method yields more stable, consistent, and accurate results compared to LIME.
Multiple-Source Localization from a Single-Snapshot Observation Using Graph Bayesian Optimization
PDF ↗Due to the significance of its various applications, source localization has garnered considerable attention as one of the most important means to confront diffusion hazards. Multi-source localization from a single-snapshot observation is especially relevant due to its prevalence. However, the inherent complexities of this problem, such as limited information, interactions among sources, and dependence on diffusion models, pose challenges to resolution. Current methods typically utilize heuristics and greedy selection, and they are usually bonded with one diffusion model. Consequently, their effectiveness is constrained. To address these limitations, we propose a simulation-based method termed BOSouL. Bayesian optimization (BO) is adopted to approximate the results for its sample efficiency. A surrogate function models uncertainty from the limited information. It takes sets of nodes as the input instead of individual nodes. BOSouL can incorporate any diffusion model in the data acquisition process through simulations. Empirical studies demonstrate that its performance is robust across graph structures and diffusion models. The code is available at https://github.com/XGraph-Team/BOSouL.
Identifying and Addressing Disparities in Public Libraries with Bayesian Latent Variable Modeling
PDF ↗Public libraries are an essential public good. We ask: are urban library systems providing equitable service to all residents, in terms of the books they have access to and check out? If not, what causes disparities: heterogeneous book collections, resident behavior and access, and/or operational policies? Existing methods leverage only system-level outcome data (such as overall checkouts per branch), and so cannot distinguish between these factors. As a result, it is difficult to use their results to guide interventions to increase equitable access. We propose a Bayesian framework to characterize book checkout behavior across multiple branches of a library system, learning heterogeneous book popularity, overall branch demand, and usage of the online hold system, while controlling for book availability. In collaboration with the New York Public Library, we apply our framework to granular data consisting of over 400,000 checkouts during 2022. We first show that our model significantly out-performs baseline methods in predicting checkouts at the book-branch level. Next, we study spatial and socioeconomic disparities. We show that disparities are largely driven by disparate use of the online holds system, which allows library patrons to receive books from any other branch through an online portal. This system thus leads to a large outflow of popular books from branches in lower income neighborhoods to those in high income ones. Finally, we illustrate the use of our model and insights to quantify the impact of potential interventions, such as changing how books are internally routed between branches to fulfill hold requests.
Optimizing the configuration and placement of sensors is crucial for reliable fall detection, indoor localization, and activity recognition in assisted living spaces. We propose a novel, sample-efficient approach to find a high-quality sensor placement in an arbitrary indoor space based on grey-box Bayesian optimization and simulation-based evaluation. Our key technical contribution lies in capturing domain-specific knowledge about the spatial distribution of activities and incorporating it into the iterative selection of query points in Bayesian optimization. Considering two simulated indoor environments and a real-world dataset containing human activities and sensor triggers, we show that our proposed method performs better compared to state-of-the-art black-box optimization techniques in identifying high-quality sensor placements, leading to an accurate activity recognition model in terms of F1-score, while also requiring a significantly lower (51.3% on average) number of expensive function queries.
Knowledge Graphs (KGs) provide a widely used format for representing entities and their relationships and have found use in diverse applications including question answering and recommendation. A majority of current research on KG inference has focused on reasoning with atomic facts (triples) and has disregarded the possibility of making complex evidential observations involving logical operators (negation, conjunction, disjunction) and quantifiers (existential, universal). Further, while the application of complex evidence has been explored in KG-based query answering (KGQA) research, in many practical online settings, observations are made sequentially. For example, in KGQA, additional context may be incrementally suggested to narrow down the answer. Or in interactive recommendation, user critiques may be expressed sequentially in order to narrow down a set of preferred items. Both settings are indicative of information filtering or tracking tasks that are reminiscent of belief tracking in Bayesian inference. In fact, in this paper, we precisely cast the problem of belief tracking over unknown KG entities given incremental complex KG evidence as a Bayesian filtering problem. Specifically, we leverage Knowledge-based Model Construction (KBMC) over the logical KG evidence to instantiate a Markov Random Field (MRF) likelihood representation to perform closed-form Bayesian inference with complex KG evidence (BIKG). We experimentally evaluate BIKG in incremental KGQA and interactive recommendation tasks demonstrating that it outperforms non-incremental methodologies and leads to better incorporation of conjunctive evidence vs. existing complex KGQA methods like CQD that leverage fuzzy T-norm operators. Overall, this work demonstrates a novel, efficient, and unified perspective of logic, KGs, and online inference through the lens of closed-form BIKG.
This study proposes and evaluates a new Bayesian network classifier (BNC) having an I-map structure with the fewest class variable parameters among all structures for which the class variable has no parent. Moreover, a new learning algorithm to learn our proposed model is presented. The proposed method is guaranteed to obtain the true classification probability asymptotically. Moreover, the method has lower computational costs than those of exact learning BNC using marginal likelihood. Comparison experiments have demonstrated the superior performance of the proposed method.
Identifying root causes of anomalies in causal processes is vital across disciplines. Once identified, one can isolate the root causes and implement necessary measures to restore the normal operation. Causal processes are often modelled as graphs with entities being nodes and their paths/interconnections as edge. Existing work only consider the contribution of nodes in the generative process, thus can not attribute the outlier score to the edges of the mechanism if the anomaly occurs in the connections. In this paper, we consider both individual edge and node of each mechanism when identifying the root causes. We introduce a noisy functional causal model to account for this purpose. Then, we employ Bayesian learning and inference methods to infer the noises of the nodes and edges. We then represent the functional form of a target outlier leaf as a function of the node and edge noises. Finally, we propose an efficient gradient-based attribution method to compute the anomaly attribution scores which scales linearly with the number of nodes and edges. Experiments on simulated datasets and two real-world scenario datasets show better anomaly attribution performance of the proposed method compared to the baselines. Our method scales to larger graphs with more nodes and edges.
Uncertainty Quantification in Heterogeneous Treatment Effect Estimation with Gaussian-Process-Based Partially Linear Model
PDF ↗Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in treatment effect estimation to support decision-making in a relatively small sample size setting. Our proposed model places Gaussian process priors on the nonparametric components of a semiparametric model called a partially linear model. This model formulation has three advantages. First, we can analytically compute the posterior distribution of a treatment effect without relying on the computationally demanding posterior approximation. Second, we can guarantee that the posterior distribution concentrates around the true one as the sample size goes to infinity. Third, we can incorporate prior knowledge about a treatment effect into the prior distribution, improving the estimation efficiency. Our experimental results show that even in the small sample size setting, our method can accurately estimate the heterogeneous treatment effects and effectively quantify its estimation uncertainty.
Training data in federated learning (FL) frameworks can have label noise, since they must be stored and annotated on clients' devices. If trained over such corrupted data, the models learn the wrong knowledge of label noise, which highly degrades their performance. Although several FL schemes are designed to combat label noise, they suffer performance degradation when the clients' devices only have limited local training samples. To this end, a new scheme called federated label-noise learning (FedLNL) is developed in this paper. The key problem of FedLNL is how to estimate a noise transition matrix (NTM) accurately in the case of limited local training samples. If a gradient-based update method is used to update the local NTM on each client's device, it can generate too large gradients for the local NTM, causing a high estimation error of the local NTM. To tackle this issue, an alternating update method for the local NTM and the local classifier is designed in FedLNL, where the local NTM is updated by a Bayesian inference-based update method. Such an alternating update method makes the loss function of existing NTM-based schemes not applicable to FedLNL. To enable federated optimization of FedLNL, a new regularizer on the parameters of the classifier called local diversity product regularizer is designed for the loss function of FedLNL. The results show that FedLNL improves the test accuracy of a trained model by up to 25.98%, compared with the state-of-the-art FL schemes that tackle label-noise issues.
Out-of-distribution (OOD) generalization has long been a challenging problem that remains largely unsolved. Gaussian processes (GP), as popular probabilistic model classes, especially in the small data regime, presume strong OOD generalization abilities. Surprisingly, their OOD generalization abilities have been under-explored before compared with other lines of GP research. In this paper, we identify that GP is not free from the problem and propose a domain invariant learning algorithm for Gaussian processes (DIL-GP) with a min-max optimization on the likelihood. DIL-GP discovers the heterogeneity in the data and forces invariance across partitioned subsets of data. We further extend the DIL-GP to improve Bayesian optimization's adaptability on changing environments. Numerical experiments demonstrate the superiority of DIL-GP for predictions on several synthetic and real-world datasets. We further demonstrate the effectiveness of the DIL-GP Bayesian optimization method on a PID parameters tuning experiment for a quadrotor. The full version and source code are available at: https://github.com/Billzxl/DIL-GP.
The theory of Bayesian learning incorporates the use of Student-t Processes to model heavy-tailed distributions and datasets with outliers. However, despite Student-t Processes having a similar computational complexity as Gaussian Processes, there has been limited emphasis on the sparse representation of this model. This is mainly due to the increased difficulty in modeling and computation compared to previous sparse Gaussian Processes. Our motivation is to address the need for a sparse representation framework that reduces computational complexity, allowing Student-t Processes to be more flexible for real-world datasets. To achieve this, we leverage the conditional distribution of Student-t Processes to introduce sparse inducing points. Bayesian methods and variational inference are then utilized to derive a well-defined lower bound, facilitating more efficient optimization of our model through stochastic gradient descent. We propose two methods for computing the variational lower bound, one utilizing Monte Carlo sampling and the other employing Jensen's inequality to compute the KL regularization term in the loss function. We propose adopting these approaches as viable alternatives to Gaussian processes when the data might contain outliers or exhibit heavy-tailed behavior, and we provide specific recommendations for their applicability. We evaluate the two proposed approaches on various synthetic and real-world datasets from UCI and Kaggle, demonstrating their effectiveness compared to baseline methods in terms of computational complexity and accuracy, as well as their robustness to outliers.
Constrained Bayesian Optimization under Partial Observations: Balanced Improvements and Provable Convergence
PDF ↗The partially observable constrained optimization problems (POCOPs) impede data-driven optimization techniques since an infeasible solution of POCOPs can provide little information about the objective as well as the constraints. We endeavor to design an efficient and provable method for expensive POCOPs under the framework of constrained Bayesian optimization. Our method consists of two key components. Firstly, we present an improved design of the acquisition functions that introduce balanced exploration during optimization. We rigorously study the convergence properties of this design to demonstrate its effectiveness. Secondly, we propose Gaussian processes embedding different likelihoods as the surrogate model for partially observable constraints. This model leads to a more accurate representation of the feasible regions compared to traditional classification-based models. Our proposed method is empirically studied on both synthetic and real-world problems. The results demonstrate the competitiveness of our method for solving POCOPs.
Few-shot learning (FSL) is essential in many practical applications. However, the limited training examples make the models more vulnerable to label noise, which can lead to poor generalization capability. To address this critical challenge, we propose a curriculum meta-learning model that employs a novel dual-level class-example sampling strategy to create a robust curriculum for adaptive task distribution formulation and robust model training. The dual-level framework proposes a heuristic class sampling criterion that measures pairwise class boundary complexity to form a class curriculum; it uses effective example sampling through an under-trained proxy model to form an example curriculum. By utilizing both class-level and example-level information, our approach is more robust to handle limited training data and noisy labels that commonly occur in few-shot learning tasks. The model has efficient convergence behavior, which is verified through rigorous convergence analysis. Additionally, we establish a novel error bound through a hierarchical PAC-Bayesian analysis for curriculum meta-learning under noise. We conduct extensive experiments that demonstrate the effectiveness of our framework in outperforming existing noisy few-shot learning methods under various few-shot classification benchmarks. Our code is available at https://github.com/ritmininglab/DCML.
While modern biotechnologies allow synthesizing new proteins and function measurements at scale, efficiently exploring a protein sequence space and engineering it remains a daunting task due to the vast sequence space of any given protein. Protein engineering is typically conducted through an iterative process of adding mutations to the wild-type or lead sequences, recombination of mutations, and running new rounds of screening. To enhance the efficiency of such a process, we propose a tree search-based bandit learning method, which expands a tree starting from the initial sequence with the guidance of a bandit machine learning model. Under simplified assumptions and a Gaussian Process prior, we provide theoretical analysis and a Bayesian regret bound, demonstrating that the method can efficiently discover a near-optimal design. The full algorithm is compatible with a suite of randomized tree search heuristics, machine learning models, pre-trained embeddings, and bandit techniques. We test various instances of the algorithm across benchmark protein datasets using simulated screens. Experiment results demonstrate that the algorithm is both sample-efficient, diversity-promoting, and able to find top designs using reasonably small mutation counts.
There are a lot of real-world black-box optimization problems that need to optimize multiple criteria simultaneously. However, in a multi-objective optimization (MOO) problem, identifying the whole Pareto front requires the prohibitive search cost, while in many practical scenarios, the decision maker (DM) only needs a specific solution among the set of the Pareto optimal solutions. We propose a Bayesian optimization (BO) approach to identifying the most preferred solution in the MOO with expensive objective functions, in which a Bayesian preference model of the DM is adaptively estimated by an interactive manner based on the two types of supervisions called the pairwise preference and improvement request. To explore the most preferred solution, we define an acquisition function in which the uncertainty both in the objective function and the DM preference is incorporated. Further, to minimize the interaction cost with the DM, we also propose an active learning strategy for the preference estimation. We empirically demonstrate the effectiveness of our proposed method through the benchmark function optimization and the hyper-parameter optimization problems for machine learning models.
In practical compressed sensing (CS), the obtained measurements typically necessitate quantization to a limited number of bits prior to transmission or storage. This nonlinear quantization process poses significant recovery challenges, particularly with extreme coarse quantization such as 1-bit. Recently, an efficient algorithm called QCS-SGM was proposed for quantized CS (QCS) which utilizes score-based generative models (SGM) as an implicit prior. Due to the adeptness of SGM in capturing the intricate structures of natural signals, QCS-SGM substantially outperforms previous QCS methods. However, QCS-SGM is constrained to (approximately) row-orthogonal sensing matrices as the computation of the likelihood score becomes intractable otherwise. To address this limitation, we introduce an advanced variant of QCS-SGM, termed QCS-SGM+, capable of handling general matrices effectively. The key idea is a Bayesian inference perspective on the likelihood score computation, wherein expectation propagation is employed for its approximate computation. Extensive experiments are conducted, demonstrating the substantial superiority of QCS-SGM+ over QCS-SGM for general sensing matrices beyond mere row-orthogonality.