In Bayesian probabilistic programming, a central problem is to estimate the normalised posterior distribution (NPD) of a probabilistic program with conditioning. Prominent approximate approaches to address this problem include Markov chain Monte Carlo and variational inference, but neither can generate guaranteed outcomes within limited time. Moreover, most existing formal approaches that perform exact inference for NPD are restricted to programs with closed-form solutions or bounded loops/recursion. A recent work (Beutner et al., PLDI 2022) derived guaranteed bounds for NPD over programs with unbounded recursion. However, as this approach requires recursion unrolling, it suffers from the path explosion problem. Furthermore, previous approaches do not consider score-recursive probabilistic programs that allow score statements inside loops, which is non-trivial and requires careful treatment to ensure the integrability of the normalising constant in NPD. In this work, we propose a novel automated approach to derive bounds for NPD via polynomial templates. Our approach can handle probabilistic programs with unbounded while loops and continuous distributions with infinite supports. The novelties in our approach are three-fold: First, we use polynomial templates to circumvent the path explosion problem from recursion unrolling; Second, we derive a novel multiplicative variant of Optional Stopping Theorem that addresses the integrability issue in score-recursive programs; Third, to increase the accuracy of the derived bounds via polynomial templates, we propose a novel technique of truncation that truncates a program into a bounded range of program values. Experiments over a wide range of benchmarks demonstrate that our approach is time-efficient and can derive bounds for NPD that are comparable with (or tighter than) the recursion-unrolling approach (Beutner et al., PLDI 2022).
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We consider the problem of signal estimation in a generalized linear model (GLM). GLMs include many canonical problems in statistical estimation, such as linear regression, phase retrieval, and 1-bit compressed sensing. Recent work has precisely characterized the asymptotic minimum mean-squared error (MMSE) for GLMs with i.i.d. Gaussian sensing matrices. However, in many models there is a significant gap between the MMSE and the performance of the best known feasible estimators. In this work, we address this issue by considering GLMs defined via spatially coupled sensing matrices. We propose an efficient approximate message passing (AMP) algorithm for estimation and prove that with a simple choice of spatially coupled design, the MSE of a carefully tuned AMP estimator approaches the asymptotic MMSE in the high-dimensional limit. To prove the result, we first rigorously characterize the asymptotic performance of AMP for a GLM with a generic spatially coupled design. This characterization is in terms of a deterministic recursion (`state evolution') that depends on the parameters defining the spatial coupling. Then, using a simple spatially coupled design and judicious choice of functions defining the AMP, we analyze the fixed points of the resulting state evolution and show that it achieves the asymptotic MMSE. Numerical results for phase retrieval and rectified linear regression show that spatially coupled designs can yield substantially lower MSE than i.i.d. Gaussian designs at finite dimensions when used with AMP algorithms.
The detection of spoofing speech generated by unseen algorithms remains an unresolved challenge. One reason for the lack of generalization ability is traditional detecting systems follow the binary classification paradigm, which inherently assumes the possession of prior knowledge of spoofing speech. One-class methods attempt to learn the distribution of bonafide speech and are inherently suited to the task where spoofing speech exhibits significant differences. However, training a one-class system using only bonafide speech is challenging. In this paper, we introduce a teacher-student framework to provide guidance for the training of a one-class model. The proposed one-class knowledge distillation method outperforms other state-of-the-art methods on the ASVspoof 21DF dataset and InTheWild dataset, which demonstrates its superior generalization ability.
Grasping inhomogeneous objects in real-world applications remains a challenging task due to the unknown physical properties such as mass distribution and coefficient of friction. In this study, we propose a meta-learning algorithm called ConDex, which incorporates Conditional Neural Processes (CNP) with DexNet-2.0 to autonomously discern the underlying physical properties of objects using depth images. ConDex efficiently acquires physical embeddings from limited trials, enabling precise grasping point estimation. Furthermore, ConDex is capable of updating the predicted grasping quality iteratively from new trials in an online fashion. To the best of our knowledge, we are the first who generate two object datasets focusing on inhomogeneous physical properties with varying mass distributions and friction coefficients. Extensive evaluations in simulation demonstrate ConDex's superior performance over DexNet-2.0 and existing meta-learning-based grasping pipelines. Furthermore, ConDex shows robust generalization to previously unseen real-world objects despite training solely in the simulation. The synthetic and real-world datasets will be published as well.
The physical layer authentication (PLA) is a promising technology which can enhance the access security of a massive number of devices in the near future. In this paper, we propose a reconfigurable intelligent surface (RIS)-assisted PLA system, in which the legitimate transmitter can customize the channel fingerprints during PLA by controlling the ON-OFF state of the RIS. Without loss of generality, we use the received signal strength (RSS) based spoofing detection approach to analyze the feasibility of the proposed architecture. Specifically, based on the RSS, we derive the statistical properties of PLA and give some interesting insights, which showcase that the RIS-assisted PLA is theoretically feasible. Then, we derive the optimal detection threshold to maximize the performance in the context of the presented performance metrics. Next, the actual feasibility of the proposed system is verified via proof-of-concept experiments on a RIS-assisted PLA prototype platform. The experiment results show that there are 3.5% and 76% performance improvements when the transmission sources are at different locations and at the same location, respectively.
We consider a decentralized formulation of the active hypothesis testing (AHT) problem, where multiple agents gather noisy observations from the environment with the purpose of identifying the correct hypothesis. At each time step, agents have the option to select a sampling action. These different actions result in observations drawn from various distributions, each associated with a specific hypothesis. The agents collaborate to accomplish the task, where message exchanges between agents are allowed over a rate-limited communications channel. The objective is to devise a multi-agent policy that minimizes the Bayes risk. This risk comprises both the cost of sampling and the joint terminal cost incurred by the agents upon making a hypothesis declaration. Deriving optimal structured policies for AHT problems is generally mathematically intractable, even in the context of a single agent. As a result, recent efforts have turned to deep learning methodologies to address these problems, which have exhibited significant success in single-agent learning scenarios. In this paper, we tackle the multi-agent AHT formulation by introducing a novel algorithm rooted in the framework of deep multi-agent reinforcement learning. This algorithm, named Multi-Agent Reinforcement Learning for AHT (MARLA), operates at each time step by having each agent map its state to an action (sampling rule or stopping rule) using a trained deep neural network with the goal of minimizing the Bayes risk. We present a comprehensive set of experimental results that effectively showcase the agents' ability to learn collaborative strategies and enhance performance using MARLA. Furthermore, we demonstrate the superiority of MARLA over single-agent learning approaches. Finally, we provide an open-source implementation of the MARLA framework, for the benefit of researchers and developers in related domains.
We show a cancellation property for probabilistic choice. If distributions mu + rho and nu + rho are branching probabilistic bisimilar, then distributions mu and nu are also branching probabilistic bisimilar. We do this in the setting of a basic process language involving non-deterministic and probabilistic choice and define branching probabilistic bisimilarity on distributions. Despite the fact that the cancellation property is very elegant and concise, we failed to provide a short and natural combinatorial proof. Instead we provide a proof using metric topology. Our major lemma is that every distribution can be unfolded into an equivalent stable distribution, where the topological arguments are required to deal with uncountable branching.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
In semi-supervised domain adaptation, a few labeled samples per class in the target domain guide features of the remaining target samples to aggregate around them. However, the trained model cannot produce a highly discriminative feature representation for the target domain because the training data is dominated by labeled samples from the source domain. This could lead to disconnection between the labeled and unlabeled target samples as well as misalignment between unlabeled target samples and the source domain. In this paper, we propose a novel approach called Cross-domain Adaptive Clustering to address this problem. To achieve both inter-domain and intra-domain adaptation, we first introduce an adversarial adaptive clustering loss to group features of unlabeled target data into clusters and perform cluster-wise feature alignment across the source and target domains. We further apply pseudo labeling to unlabeled samples in the target domain and retain pseudo-labels with high confidence. Pseudo labeling expands the number of ``labeled" samples in each class in the target domain, and thus produces a more robust and powerful cluster core for each class to facilitate adversarial learning. Extensive experiments on benchmark datasets, including DomainNet, Office-Home and Office, demonstrate that our proposed approach achieves the state-of-the-art performance in semi-supervised domain adaptation.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
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.
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