We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a stochastic differential equation evolution. The score term is given in closed form by a regularized Wasserstein proximal, using a kernel convolution that is approximated by sampling. We demonstrate fast convergence on various problems and show improved dimensional dependence of mixing time bounds for the case of Gaussian distributions compared to the unadjusted Langevin algorithm (ULA) and the Metropolis-adjusted Langevin algorithm (MALA). We additionally derive closed form expressions for the distributions at each iterate for quadratic potential functions, characterizing the variance reduction. Empirical results demonstrate that the particles behave in an organized manner, lying on level set contours of the potential. Moreover, the posterior mean estimator of the proposed method is shown to be closer to the maximum a-posteriori estimator compared to ULA and MALA in the context of Bayesian logistic regression. Additional examples demonstrate competitive performance for Bayesian neural network training.
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Recovering masked feedback with neural models is a popular paradigm in recommender systems. Seeing the success of diffusion models in solving ill-posed inverse problems, we introduce a conditional diffusion framework for collaborative filtering that iteratively reconstructs a user's hidden preferences guided by its historical interactions. To better align with the intrinsic characteristics of implicit feedback data, we implement forward diffusion by applying synthetic smoothing filters to interaction signals on an item-item graph. The resulting reverse diffusion can be interpreted as a personalized process that gradually refines preference scores. Through graph Fourier transform, we equivalently characterize this model as an anisotropic Gaussian diffusion in the graph spectral domain, establishing both forward and reverse formulations. Our model outperforms state-of-the-art methods by a large margin on one dataset and yields competitive results on the others.
Spectral bounds form a powerful tool to estimate the minimum distances of quasi-cyclic codes. They generalize the defining set bounds of cyclic codes to those of quasi-cyclic codes. Based on the eigenvalues of quasi-cyclic codes and the corresponding eigenspaces, we provide an improved spectral bound for quasi-cyclic codes. Numerical results verify that the improved bound outperforms the Jensen bound in almost all cases. Based on the improved bound, we propose a general construction of quasi-cyclic codes with excellent designed minimum distances. For the quasi-cyclic codes produced by this general construction, the improved spectral bound is always sharper than the Jensen bound.
Probabilistic couplings are the foundation for many probabilistic relational program logics and arise when relating random sampling statements across two programs. In relational program logics, this manifests as dedicated coupling rules that, e.g., say we may reason as if two sampling statements return the same value. However, this approach fundamentally requires aligning or "synchronizing" the sampling statements of the two programs which is not always possible. In this paper, we develop Clutch, a higher-order probabilistic relational separation logic that addresses this issue by supporting asynchronous probabilistic couplings. We use Clutch to develop a logical step-indexed logical relational to reason about contextual refinement and equivalence of higher-order programs written in a rich language with higher-order local state and impredicative polymorphism. Finally, we demonstrate the usefulness of our approach on a number of case studies. All the results that appear in the paper have been formalized in the Coq proof assistant using the Coquelicot library and the Iris separation logic framework.
Out-of-distribution (OOD) detection is essential in identifying test samples that deviate from the in-distribution (ID) data upon which a standard network is trained, ensuring network robustness and reliability. This paper introduces OOD knowledge distillation, a pioneering learning framework applicable whether or not training ID data is available, given a standard network. This framework harnesses OOD-sensitive knowledge from the standard network to craft a binary classifier adept at distinguishing between ID and OOD samples. To accomplish this, we introduce Confidence Amendment (CA), an innovative methodology that transforms an OOD sample into an ID one while progressively amending prediction confidence derived from the standard network. This approach enables the simultaneous synthesis of both ID and OOD samples, each accompanied by an adjusted prediction confidence, thereby facilitating the training of a binary classifier sensitive to OOD. Theoretical analysis provides bounds on the generalization error of the binary classifier, demonstrating the pivotal role of confidence amendment in enhancing OOD sensitivity. Extensive experiments spanning various datasets and network architectures confirm the efficacy of the proposed method in detecting OOD samples.
Unsupervised clustering is widely used to explore large corpora, but existing formulations neither consider the users' goals nor explain clusters' meanings. We propose a new task formulation, "Goal-Driven Clustering with Explanations" (GoalEx), which represents both the goal and the explanations as free-form language descriptions. For example, to categorize the errors made by a summarization system, the input to GoalEx is a corpus of annotator-written comments for system-generated summaries and a goal description "cluster the comments based on why the annotators think the summary is imperfect.''; the outputs are text clusters each with an explanation ("this cluster mentions that the summary misses important context information."), which relates to the goal and precisely explain which comments should (not) belong to a cluster. To tackle GoalEx, we prompt a language model with "[corpus subset] + [goal] + Brainstorm a list of explanations each representing a cluster."; then we classify whether each sample belongs to a cluster based on its explanation; finally, we use integer linear programming to select a subset of candidate clusters to cover most samples while minimizing overlaps. Under both automatic and human evaluation on corpora with or without labels, our method produces more accurate and goal-related explanations than prior methods. We release our data and implementation at //github.com/ZihanWangKi/GoalEx.
Whenever a binary classifier is used to provide decision support, it typically provides both a label prediction and a confidence value. Then, the decision maker is supposed to use the confidence value to calibrate how much to trust the prediction. In this context, it has been often argued that the confidence value should correspond to a well calibrated estimate of the probability that the predicted label matches the ground truth label. However, multiple lines of empirical evidence suggest that decision makers have difficulties at developing a good sense on when to trust a prediction using these confidence values. In this paper, our goal is first to understand why and then investigate how to construct more useful confidence values. We first argue that, for a broad class of utility functions, there exist data distributions for which a rational decision maker is, in general, unlikely to discover the optimal decision policy using the above confidence values -- an optimal decision maker would need to sometimes place more (less) trust on predictions with lower (higher) confidence values. However, we then show that, if the confidence values satisfy a natural alignment property with respect to the decision maker's confidence on her own predictions, there always exists an optimal decision policy under which the level of trust the decision maker would need to place on predictions is monotone on the confidence values, facilitating its discoverability. Further, we show that multicalibration with respect to the decision maker's confidence on her own predictions is a sufficient condition for alignment. Experiments on four different AI-assisted decision making tasks where a classifier provides decision support to real human experts validate our theoretical results and suggest that alignment may lead to better decisions.
Nonresponse after probability sampling is a universal challenge in survey sampling, often necessitating adjustments to mitigate sampling and selection bias simultaneously. This study explored the removal of bias and effective utilization of available information, not just in nonresponse but also in the scenario of data integration, where summary statistics from other data sources are accessible. We reformulate these settings within a two-step monotone missing data framework, where the first step of missingness arises from sampling and the second originates from nonresponse. Subsequently, we derive the semiparametric efficiency bound for the target parameter. We also propose adaptive estimators utilizing methods of moments and empirical likelihood approaches to attain the lower bound. The proposed estimator exhibits both efficiency and double robustness. However, attaining efficiency with an adaptive estimator requires the correct specification of certain working models. To reinforce robustness against the misspecification of working models, we extend the property of double robustness to multiple robustness by proposing a two-step empirical likelihood method that effectively leverages empirical weights. A numerical study is undertaken to investigate the finite-sample performance of the proposed methods. We further applied our methods to a dataset from the National Health and Nutrition Examination Survey data by efficiently incorporating summary statistics from the National Health Interview Survey data.
Integrating and processing information from various sources or modalities are critical for obtaining a comprehensive and accurate perception of the real world. Drawing inspiration from neuroscience, we develop the Information-Theoretic Hierarchical Perception (ITHP) model, which utilizes the concept of information bottleneck. Distinct from most traditional fusion models that aim to incorporate all modalities as input, our model designates the prime modality as input, while the remaining modalities act as detectors in the information pathway. Our proposed perception model focuses on constructing an effective and compact information flow by achieving a balance between the minimization of mutual information between the latent state and the input modal state, and the maximization of mutual information between the latent states and the remaining modal states. This approach leads to compact latent state representations that retain relevant information while minimizing redundancy, thereby substantially enhancing the performance of downstream tasks. Experimental evaluations on both the MUStARD and CMU-MOSI datasets demonstrate that our model consistently distills crucial information in multimodal learning scenarios, outperforming state-of-the-art benchmarks.
To facilitate efficient learning, policy gradient approaches to deep reinforcement learning (RL) are typically paired with variance reduction measures and strategies for making large but safe policy changes based on a batch of experiences. Natural policy gradient methods, including Trust Region Policy Optimization (TRPO), seek to produce monotonic improvement through bounded changes in policy outputs. Proximal Policy Optimization (PPO) is a commonly used, first-order algorithm that instead uses loss clipping to take multiple safe optimization steps per batch of data, replacing the bound on the single step of TRPO with regularization on multiple steps. In this work, we find that the performance of PPO, when applied to continuous action spaces, may be consistently improved through a simple change in objective. Instead of the importance sampling objective of PPO, we instead recommend a basic policy gradient, clipped in an equivalent fashion. While both objectives produce biased gradient estimates with respect to the RL objective, they also both display significantly reduced variance compared to the unbiased off-policy policy gradient. Additionally, we show that (1) the clipped-objective policy gradient (COPG) objective is on average "pessimistic" compared to both the PPO objective and (2) this pessimism promotes enhanced exploration. As a result, we empirically observe that COPG produces improved learning compared to PPO in single-task, constrained, and multi-task learning, without adding significant computational cost or complexity. Compared to TRPO, the COPG approach is seen to offer comparable or superior performance, while retaining the simplicity of a first-order method.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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