The variational autoencoder (VAE) typically employs a standard normal prior as a regularizer for the probabilistic latent encoder. However, the Gaussian tail often decays too quickly to effectively accommodate the encoded points, failing to preserve crucial structures hidden in the data. In this paper, we explore the use of heavy-tailed models to combat over-regularization. Drawing upon insights from information geometry, we propose $t^3$VAE, a modified VAE framework that incorporates Student's t-distributions for the prior, encoder, and decoder. This results in a joint model distribution of a power form which we argue can better fit real-world datasets. We derive a new objective by reformulating the evidence lower bound as joint optimization of KL divergence between two statistical manifolds and replacing with $\gamma$-power divergence, a natural alternative for power families. $t^3$VAE demonstrates superior generation of low-density regions when trained on heavy-tailed synthetic data. Furthermore, we show that $t^3$VAE significantly outperforms other models on CelebA and imbalanced CIFAR-100 datasets.
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Many stochastic continuous-state dynamical systems can be modeled as probabilistic programs with nonlinear non-polynomial updates in non-nested loops. We present two methods, one approximate and one exact, to automatically compute, without sampling, moment-based invariants for such probabilistic programs as closed-form solutions parameterized by the loop iteration. The exact method applies to probabilistic programs with trigonometric and exponential updates and is embedded in the Polar tool. The approximate method for moment computation applies to any nonlinear random function as it exploits the theory of polynomial chaos expansion to approximate non-polynomial updates as the sum of orthogonal polynomials. This translates the dynamical system to a non-nested loop with polynomial updates, and thus renders it conformable with the Polar tool that computes the moments of any order of the state variables. We evaluate our methods on an extensive number of examples ranging from modeling monetary policy to several physical motion systems in uncertain environments. The experimental results demonstrate the advantages of our approach with respect to the current state-of-the-art.
How many different binary classification problems a single learning algorithm can solve on a fixed data with exactly zero or at most a given number of cross-validation errors? While the number in the former case is known to be limited by the no-free-lunch theorem, we show that the exact answers are given by the theory of error detecting codes. As a case study, we focus on the AUC performance measure and leave-pair-out cross-validation (LPOCV), in which every possible pair of data with different class labels is held out at a time. We shown that the maximal number of classification problems with fixed class proportion, for which a learning algorithm can achieve zero LPOCV error, equals the maximal number of code words in a constant weight code (CWC), with certain technical properties. We then generalize CWCs by introducing light CWCs and prove an analogous result for nonzero LPOCV errors and light CWCs. Moreover, we prove both upper and lower bounds on the maximal numbers of code words in light CWCs. Finally, as an immediate practical application, we develop new LPOCV based randomization tests for learning algorithms that generalize the classical Wilcoxon-Mann-Whitney U test.
We propose policy gradient algorithms for robust infinite-horizon Markov decision processes (MDPs) with non-rectangular uncertainty sets, thereby addressing an open challenge in the robust MDP literature. Indeed, uncertainty sets that display statistical optimality properties and make optimal use of limited data often fail to be rectangular. Unfortunately, the corresponding robust MDPs cannot be solved with dynamic programming techniques and are in fact provably intractable. We first present a randomized projected Langevin dynamics algorithm that solves the robust policy evaluation problem to global optimality but is inefficient. We also propose a deterministic policy gradient method that is efficient but solves the robust policy evaluation problem only approximately, and we prove that the approximation error scales with a new measure of non-rectangularity of the uncertainty set. Finally, we describe an actor-critic algorithm that finds an $\epsilon$-optimal solution for the robust policy improvement problem in $\mathcal{O}(1/\epsilon^4)$ iterations. We thus present the first complete solution scheme for robust MDPs with non-rectangular uncertainty sets offering global optimality guarantees. Numerical experiments show that our algorithms compare favorably against state-of-the-art methods.
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work, we build on widely adopted $k$-center clustering and model its input background knowledge as must-link (ML) and cannot-link (CL) constraint sets. However, most clustering problems including $k$-center are inherently $\mathcal{NP}$-hard, while the more complex constrained variants are known to suffer severer approximation and computation barriers that significantly limit their applicability. By employing a suite of techniques including reverse dominating sets, linear programming (LP) integral polyhedron, and LP duality, we arrive at the first efficient approximation algorithm for constrained $k$-center with the best possible ratio of 2. We also construct competitive baseline algorithms and empirically evaluate our approximation algorithm against them on a variety of real datasets. The results validate our theoretical findings and demonstrate the great advantages of our algorithm in terms of clustering cost, clustering quality, and running time.
Diffusion models have emerged as powerful generative tools, rivaling GANs in sample quality and mirroring the likelihood scores of autoregressive models. A subset of these models, exemplified by DDIMs, exhibit an inherent asymmetry: they are trained over $T$ steps but only sample from a subset of $T$ during generation. This selective sampling approach, though optimized for speed, inadvertently misses out on vital information from the unsampled steps, leading to potential compromises in sample quality. To address this issue, we present the S$^{2}$-DMs, which is a new training method by using an innovative $L_{skip}$, meticulously designed to reintegrate the information omitted during the selective sampling phase. The benefits of this approach are manifold: it notably enhances sample quality, is exceptionally simple to implement, requires minimal code modifications, and is flexible enough to be compatible with various sampling algorithms. On the CIFAR10 dataset, models trained using our algorithm showed an improvement of 3.27% to 14.06% over models trained with traditional methods across various sampling algorithms (DDIMs, PNDMs, DEIS) and different numbers of sampling steps (10, 20, ..., 1000). On the CELEBA dataset, the improvement ranged from 8.97% to 27.08%. Access to the code and additional resources is provided in the github.
The advancement of natural language processing (NLP) has been significantly boosted by the development of transformer-based large language models (LLMs). These models have revolutionized NLP tasks, particularly in code generation, aiding developers in creating software with enhanced efficiency. Despite their advancements, challenges in balancing code snippet generation with effective test case generation and execution persist. To address these issues, this paper introduces Multi-Agent Assistant Code Generation (AgentCoder), a novel solution comprising a multi-agent framework with specialized agents: the programmer agent, the test designer agent, and the test executor agent. During the coding procedure, the programmer agent will focus on the code generation and refinement based on the test executor agent's feedback. The test designer agent will generate test cases for the generated code, and the test executor agent will run the code with the test cases and write the feedback to the programmer. This collaborative system ensures robust code generation, surpassing the limitations of single-agent models and traditional methodologies. Our extensive experiments on 9 code generation models and 12 enhancement approaches showcase AgentCoder's superior performance over existing code generation models and prompt engineering techniques across various benchmarks. For example, AgentCoder achieves 77.4% and 89.1% pass@1 in HumanEval-ET and MBPP-ET with GPT-3.5, while SOTA baselines obtain only 69.5% and 63.0%.
Annotating automatic target recognition (ATR) is a highly challenging task, primarily due to the unavailability of labeled data in the target domain. Hence, it is essential to construct an optimal target domain classifier by utilizing the labeled information of the source domain images. The transductive transfer learning (TTL) method that incorporates a CycleGAN-based unpaired domain translation network has been previously proposed in the literature for effective ATR annotation. Although this method demonstrates great potential for ATR, it severely suffers from lower annotation performance, higher Fr\'echet Inception Distance (FID) score, and the presence of visual artifacts in the synthetic images. To address these issues, we propose a hybrid contrastive learning base unpaired domain translation (H-CUT) network that achieves a significantly lower FID score. It incorporates both attention and entropy to emphasize the domain-specific region, a noisy feature mixup module to generate high variational synthetic negative patches, and a modulated noise contrastive estimation (MoNCE) loss to reweight all negative patches using optimal transport for better performance. Our proposed contrastive learning and cycle-consistency-based TTL (C3TTL) framework consists of two H-CUT networks and two classifiers. It simultaneously optimizes cycle-consistency, MoNCE, and identity losses. In C3TTL, two H-CUT networks have been employed through a bijection mapping to feed the reconstructed source domain images into a pretrained classifier to guide the optimal target domain classifier. Extensive experimental analysis conducted on three ATR datasets demonstrates that the proposed C3TTL method is effective in annotating civilian and military vehicles, as well as ship targets.
Extreme multi-label text classification (XMC) aims to tag each input text with the most relevant labels from an extremely large label set, such as those that arise in product categorization and e-commerce recommendation. Recently, pretrained language representation models such as BERT achieve remarkable state-of-the-art performance across a wide range of NLP tasks including sentence classification among small label sets (typically fewer than thousands). Indeed, there are several challenges in applying BERT to the XMC problem. The main challenges are: (i) the difficulty of capturing dependencies and correlations among labels, whose features may come from heterogeneous sources, and (ii) the tractability to scale to the extreme label setting as the model size can be very large and scale linearly with the size of the output space. To overcome these challenges, we propose X-BERT, the first feasible attempt to finetune BERT models for a scalable solution to the XMC problem. Specifically, X-BERT leverages both the label and document text to build label representations, which induces semantic label clusters in order to better model label dependencies. At the heart of X-BERT is finetuning BERT models to capture the contextual relations between input text and the induced label clusters. Finally, an ensemble of the different BERT models trained on heterogeneous label clusters leads to our best final model. Empirically, on a Wiki dataset with around 0.5 million labels, X-BERT achieves new state-of-the-art results where the precision@1 reaches 67:80%, a substantial improvement over 32.58%/60.91% of deep learning baseline fastText and competing XMC approach Parabel, respectively. This amounts to a 11.31% relative improvement over Parabel, which is indeed significant since the recent approach SLICE only has 5.53% relative improvement.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
Most existing works in visual question answering (VQA) are dedicated to improving the accuracy of predicted answers, while disregarding the explanations. We argue that the explanation for an answer is of the same or even more importance compared with the answer itself, since it makes the question and answering process more understandable and traceable. To this end, we propose a new task of VQA-E (VQA with Explanation), where the computational models are required to generate an explanation with the predicted answer. We first construct a new dataset, and then frame the VQA-E problem in a multi-task learning architecture. Our VQA-E dataset is automatically derived from the VQA v2 dataset by intelligently exploiting the available captions. We have conducted a user study to validate the quality of explanations synthesized by our method. We quantitatively show that the additional supervision from explanations can not only produce insightful textual sentences to justify the answers, but also improve the performance of answer prediction. Our model outperforms the state-of-the-art methods by a clear margin on the VQA v2 dataset.
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