Bayesian Inference
Reliable Decision Support using Counterfactual Models
Decision-makers are faced with the challenge of estimating what is likely to happen when they take an action. For instance, if I choose not to treat this patient, are they likely to die? Practitioners commonly use supervised learning algorithms to fit predictive models that help decision-makers reason about likely future outcomes, but we show that this approach is unreliable, and sometimes even dangerous. The key issue is that supervised learning algorithms are highly sensitive to the policy used to choose actions in the training data, which causes the model to capture relationships that do not generalize. We propose using a different learning objective that predicts counterfactuals instead of predicting outcomes under an existing action policy as in supervised learning. To support decision-making in temporal settings, we introduce the Counterfactual Gaussian Process (CGP) to predict the counterfactual future progression of continuous-time trajectories under sequences of future actions. We demonstrate the benefits of the CGP on two important decision-support tasks: risk prediction and "what if?" reasoning for individualized treatment planning.
Mimicking Human Intuition: Cognitive Belief-Driven Q-Learning
Gu, Xingrui, Qiao, Guanren, Jiang, Chuyi, Xia, Tianqing, Mao, Hangyu
Reinforcement learning encounters challenges in various environments related to robustness and explainability. Traditional Q-learning algorithms cannot effectively make decisions and utilize the historical learning experience. To overcome these limitations, we propose Cognitive Belief-Driven Q-Learning (CBDQ), which integrates subjective belief modeling into the Q-learning framework, enhancing decision-making accuracy by endowing agents with human-like learning and reasoning capabilities. Drawing inspiration from cognitive science, our method maintains a subjective belief distribution over the expectation of actions, leveraging a cluster-based subjective belief model that enables agents to reason about the potential probability associated with each decision. CBDQ effectively mitigates overestimated phenomena and optimizes decision-making policies by integrating historical experiences with current contextual information, mimicking the dynamics of human decision-making. We evaluate the proposed method on discrete control benchmark tasks in various complicate environments. The results demonstrate that CBDQ exhibits stronger adaptability, robustness, and human-like characteristics in handling these environments, outperforming other baselines. We hope this work will give researchers a fresh perspective on understanding and explaining Q-learning.
DaWin: Training-free Dynamic Weight Interpolation for Robust Adaptation
Oh, Changdae, Li, Yixuan, Song, Kyungwoo, Yun, Sangdoo, Han, Dongyoon
Adapting a pre-trained foundation model on downstream tasks should ensure robustness against distribution shifts without the need to retrain the whole model. Although existing weight interpolation methods are simple yet effective, we argue their static nature limits downstream performance while achieving efficiency. In this work, we propose DaWin, a training-free dynamic weight interpolation method that leverages the entropy of individual models over each unlabeled test sample to assess model expertise, and compute per-sample interpolation coefficients dynamically. Unlike previous works that typically rely on additional training to learn such coefficients, our approach requires no training. Then, we propose a mixture modeling approach that greatly reduces inference overhead raised by dynamic interpolation. We validate DaWin on the large-scale visual recognition benchmarks, spanning 14 tasks across robust fine-tuning - ImageNet and derived five distribution shift benchmarks - and multi-task learning with eight classification tasks. Results demonstrate that DaWin achieves significant performance gain in considered settings, with minimal computational overhead. We further discuss DaWin's analytic behavior to explain its empirical success. The emergence of foundation models (Bommasani et al., 2021; Radford et al., 2021; Brown et al., 2020) has significantly lowered the barrier to deploying artificial intelligence solutions across a wide range of real-world problems. Leveraging the strong general knowledge acquired through large-scale pre-training, foundation models can be efficiently adapted for numerous tasks. However, recent studies have shown that while fine-tuning improves performance on specific downstream tasks, it may often undermine the model's generalizability and robustness (Wortsman et al., 2022b). For example, a model fine-tuned on ImageNet has better accuracy on in-distribution (ID) data yet may underperform in out-of-distribution (OOD) data such as ImageNet-A (Hendrycks et al., 2021b).
Optimization Proxies using Limited Labeled Data and Training Time -- A Semi-Supervised Bayesian Neural Network Approach
Pareek, Parikshit, Sundar, Kaarthik, Deka, Deepjyoti, Misra, Sidhant
Constrained optimization problems arise in various engineering system operations such as inventory management and electric power grids. However, the requirement to repeatedly solve such optimization problems with uncertain parameters poses a significant computational challenge. This work introduces a learning scheme using Bayesian Neural Networks (BNNs) to solve constrained optimization problems under limited labeled data and restricted model training times. We propose a semi-supervised BNN for this practical but complex regime, wherein training commences in a sandwiched fashion, alternating between a supervised learning step (using labeled data) for minimizing cost, and an unsupervised learning step (using unlabeled data) for enforcing constraint feasibility. Both supervised and unsupervised steps use a Bayesian approach, where Stochastic Variational Inference is employed for approximate Bayesian inference. We show that the proposed semi-supervised learning method outperforms conventional BNN and deep neural network (DNN) architectures on important non-convex constrained optimization problems from energy network operations, achieving up to a tenfold reduction in expected maximum equality gap and halving the optimality and inequality (feasibility) gaps, without requiring any correction or projection step. By leveraging the BNN's ability to provide posterior samples at minimal computational cost, we demonstrate that a Selection via Posterior (SvP) scheme can further reduce equality gaps by more than 10%. We also provide tight and practically meaningful probabilistic confidence bounds that can be constructed using a low number of labeled testing data and readily adapted to other applications.
Back to Bayesics: Uncovering Human Mobility Distributions and Anomalies with an Integrated Statistical and Neural Framework
Duan, Minxuan, Qian, Yinlong, Zhao, Lingyi, Zhou, Zihao, Rasheed, Zeeshan, Yu, Rose, Shafique, Khurram
Existing methods for anomaly detection often fall short due to their inability to handle the complexity, heterogeneity, and high dimensionality inherent in real-world mobility data. In this paper, we propose DeepBayesic, a novel framework that integrates Bayesian principles with deep neural networks to model the underlying multivariate distributions from sparse and complex datasets. Unlike traditional models, DeepBayesic is designed to manage heterogeneous inputs, accommodating both continuous and categorical data to provide a more comprehensive understanding of mobility patterns. The framework features customized neural density estimators and hybrid architectures, allowing for flexibility in modeling diverse feature distributions and enabling the use of specialized neural networks tailored to different data types. Our approach also leverages agent embeddings for personalized anomaly detection, enhancing its ability to distinguish between normal and anomalous behaviors for individual agents. We evaluate our approach on several mobility datasets, demonstrating significant improvements over state-of-the-art anomaly detection methods. Our results indicate that incorporating personalization and advanced sequence modeling techniques can substantially enhance the ability to detect subtle and complex anomalies in spatiotemporal event sequences.
GraphIC: A Graph-Based In-Context Example Retrieval Model for Multi-Step Reasoning
Fu, Jiale, Wang, Yaqing, Han, Simeng, Fan, Jiaming, Si, Chen, Yang, Xu
In-context learning (ICL) enables large language models (LLMs) to generalize to new tasks by incorporating a few in-context examples (ICEs) directly in the input, without updating parameters. However, the effectiveness of ICL heavily relies on the selection of ICEs, and conventional text-based embedding methods are often inadequate for tasks that require multi-step reasoning, such as mathematical and logical problem solving. This is due to the bias introduced by shallow semantic similarities that fail to capture the deeper reasoning structures required for these tasks. We present GraphIC, a novel approach that leverages graph-based representations of reasoning processes, coupled with Bayesian Networks (BNs) to select ICEs. Importantly, BNs capture the dependency of a node's attributes on its parent nodes, closely mirroring the hierarchical nature of human cognition--where each thought is shaped by preceding ones. This makes BNs particularly well-suited for multi-step reasoning tasks, aligning the process more closely with human-like reasoning. Extensive experiments across three types of reasoning tasks (mathematical reasoning, code generation, and logical reasoning) demonstrate that GraphIC outperforms both training-free and training-based models in selecting ICEs, excelling in terms of both effectiveness and efficiency. We show that GraphIC enhances ICL's performance and interpretability, significantly advancing ICE selection for multi-step reasoning tasks. In-context learning (ICL) (Brown et al., 2020) represents a paradigm in how large language models (LLMs) perform inference by using a small number of in-context examples (ICEs) within the input prompt. This technique enables LLMs to generalize to new tasks or enhance their performance on existing tasks without updating parameters. However, previous studies have highlighted the sensitivity of ICL performance to the specific ICEs selected (Zhao et al., 2021; Liu et al., 2022), underscoring the importance of strategic ICE selection. Consequently, numerous methods have been proposed to optimize the selection of ICEs, focusing on improving task performance and ensuring greater robustness (Liu et al., 2022; Rubin et al., 2022; Ye et al., 2023; Gupta et al., 2024).
The Benefit of Being Bayesian in Online Conformal Prediction
Zhang, Zhiyu, Lu, Zhou, Yang, Heng
Based on the framework of Conformal Prediction (CP), we study the online construction of valid confidence sets given a black-box machine learning model. By converting the target confidence levels into quantile levels, the problem can be reduced to predicting the quantiles (in hindsight) of a sequentially revealed data sequence. Two very different approaches have been studied previously. (i) Direct approach: Assuming the data sequence is iid or exchangeable, one could maintain the empirical distribution of the observed data as an algorithmic belief, and directly predict its quantiles. (ii) Indirect approach: As statistical assumptions often do not hold in practice, a recent trend is to consider the adversarial setting and apply first-order online optimization to moving quantile losses (Gibbs & Cand\`es, 2021). It requires knowing the target quantile level beforehand, and suffers from certain validity issues on the obtained confidence sets, due to the associated loss linearization. This paper presents a novel Bayesian CP framework that combines their strengths. Without any statistical assumption, it is able to both: (i) answer multiple arbitrary confidence level queries online, with provably low regret; and (ii) overcome the validity issues suffered by first-order optimization baselines, due to being "data-centric" rather than "iterate-centric". From a technical perspective, our key idea is to regularize the algorithmic belief of the above direct approach by a Bayesian prior, which "robustifies" it by simulating a non-linearized Follow the Regularized Leader (FTRL) algorithm on the output. For statisticians, this can be regarded as an online adversarial view of Bayesian inference. Importantly, the proposed belief update backbone is shared by prediction heads targeting different confidence levels, bringing practical benefits analogous to U-calibration (Kleinberg et al., 2023).
Deep Dynamic Poisson Factorization Model
A new model, named as deep dynamic poisson factorization model, is proposed in this paper for analyzing sequential count vectors. The model based on the Poisson Factor Analysis method captures dependence among time steps by neural networks, representing the implicit distributions. Local complicated relationship is obtained from local implicit distribution, and deep latent structure is exploited to get the long-time dependence. Variational inference on latent variables and gradient descent based on the loss functions derived from variational distribution is performed in our inference. Synthetic datasets and real-world datasets are applied to the proposed model and our results show good predicting and fitting performance with interpretable latent structure.
Permutation-based Causal Inference Algorithms with Interventions
Yuhao Wang, Liam Solus, Karren Yang, Caroline Uhler
Learning directed acyclic graphs using both observational and interventional data is now a fundamentally important problem due to recent technological developments in genomics that generate such single-cell gene expression data at a very large scale. In order to utilize this data for learning gene regulatory networks, efficient and reliable causal inference algorithms are needed that can make use of both observational and interventional data. In this paper, we present two algorithms of this type and prove that both are consistent under the faithfulness assumption. These algorithms are interventional adaptations of the Greedy SP algorithm and are the first algorithms using both observational and interventional data with consistency guarantees. Moreover, these algorithms have the advantage that they are nonparametric, which makes them useful also for analyzing non-Gaussian data. In this paper, we present these two algorithms and their consistency guarantees, and we analyze their performance on simulated data, protein signaling data, and single-cell gene expression data.