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Randomized algorithms, such as randomized sketching or projections, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs, leading to the problem of evaluating their accuracy. In this paper, we develop a statistical inference framework for quantifying the uncertainty of the outputs of randomized algorithms. We develop appropriate statistical methods -- sub-randomization, multi-run plug-in and multi-run aggregation inference -- by using multiple runs of the same randomized algorithm, or by estimating the unknown parameters of the limiting distribution. As an example, we develop methods for statistical inference for least squares parameters via random sketching using matrices with i.i.d.entries, or uniform partial orthogonal matrices. For this, we characterize the limiting distribution of estimators obtained via sketch-and-solve as well as partial sketching methods. The analysis of i.i.d. sketches uses a trigonometric interpolation argument to establish a differential equation for the limiting expected characteristic function and find the dependence on the kurtosis of the entries of the sketching matrix. The results are supported via a broad range of simulations.

The assessment of regression models with discrete outcomes is challenging and has many fundamental issues. With discrete outcomes, standard regression model assessment tools such as Pearson and deviance residuals do not follow the conventional reference distribution (normal) under the true model, calling into question the legitimacy of model assessment based on these tools. To fill this gap, we construct a new type of residuals for general discrete outcomes, including ordinal and count outcomes. The proposed residuals are based on two layers of probability integral transformation. When at least one continuous covariate is available, the proposed residuals closely follow a uniform distribution (a normal distribution after transformation) under the correctly specified model. One can construct visualizations such as QQ plots to check the overall fit of a model straightforwardly, and the shape of QQ plots can further help identify possible causes of misspecification such as overdispersion. We provide theoretical justification for the proposed residuals by establishing their asymptotic properties. Moreover, in order to assess the mean structure and identify potential covariates, we develop an ordered curve as a supplementary tool, which is based on the comparison between the partial sum of outcomes and of fitted means. Through simulation, we demonstrate empirically that the proposed tools outperform commonly used residuals for various model assessment tasks. We also illustrate the workflow of model assessment using the proposed tools in data analysis.

Partial label learning (PLL) is a typical weakly supervised learning problem in which each instance is associated with a candidate label set, and among which only one is true. However, the assumption that the ground-truth label is always among the candidate label set would be unrealistic, as the reliability of the candidate label sets in real-world applications cannot be guaranteed by annotators. Therefore, a generalized PLL named Unreliable Partial Label Learning (UPLL) is proposed, in which the true label may not be in the candidate label set. Due to the challenges posed by unreliable labeling, previous PLL methods will experience a marked decline in performance when applied to UPLL. To address the issue, we propose a two-stage framework named Unreliable Partial Label Learning with Recursive Separation (UPLLRS). In the first stage, the self-adaptive recursive separation strategy is proposed to separate the training set into a reliable subset and an unreliable subset. In the second stage, a disambiguation strategy is employed to progressively identify the ground-truth labels in the reliable subset. Simultaneously, semi-supervised learning methods are adopted to extract valuable information from the unreliable subset. Our method demonstrates state-of-the-art performance as evidenced by experimental results, particularly in situations of high unreliability. Code and supplementary materials are available at //github.com/dhiyu/UPLLRS.

Machine learning algorithms have shown remarkable performance in diverse applications. However, it is still challenging to guarantee performance in distribution shifts when distributions of training and test datasets are different. There have been several approaches to improve the performance in distribution shift cases by learning invariant features across groups or domains. However, we observe that the previous works only learn invariant features partially. While the prior works focus on the limited invariant features, we first raise the importance of the sufficient invariant features. Since only training sets are given empirically, the learned partial invariant features from training sets might not be present in the test sets under distribution shift. Therefore, the performance improvement on distribution shifts might be limited. In this paper, we argue that learning sufficient invariant features from the training set is crucial for the distribution shift case. Concretely, we newly observe the connection between a) sufficient invariant features and b) flatness differences between groups or domains. Moreover, we propose a new algorithm, Adaptive Sharpness-aware Group Distributionally Robust Optimization (ASGDRO), to learn sufficient invariant features across domains or groups. ASGDRO learns sufficient invariant features by seeking common flat minima across all groups or domains. Therefore, ASGDRO improves the performance on diverse distribution shift cases. Besides, we provide a new simple dataset, Heterogeneous-CMNIST, to diagnose whether the various algorithms learn sufficient invariant features.

Voice conversion is a method that allows for the transformation of speaking style while maintaining the integrity of linguistic information. There are many researchers using deep generative models for voice conversion tasks. Generative Adversarial Networks (GANs) can quickly generate high-quality samples, but the generated samples lack diversity. The samples generated by the Denoising Diffusion Probabilistic Models (DDPMs) are better than GANs in terms of mode coverage and sample diversity. But the DDPMs have high computational costs and the inference speed is slower than GANs. In order to make GANs and DDPMs more practical we proposes DiffGAN-VC, a variant of GANs and DDPMS, to achieve non-parallel many-to-many voice conversion (VC). We use large steps to achieve denoising, and also introduce a multimodal conditional GANs to model the denoising diffusion generative adversarial network. According to both objective and subjective evaluation experiments, DiffGAN-VC has been shown to achieve high voice quality on non-parallel data sets. Compared with the CycleGAN-VC method, DiffGAN-VC achieves speaker similarity, naturalness and higher sound quality.

Sparse variational approximations are popular methods for scaling up inference and learning in Gaussian processes to larger datasets. For $N$ training points, exact inference has $O(N^3)$ cost; with $M \ll N$ features, state of the art sparse variational methods have $O(NM^2)$ cost. Recently, methods have been proposed using more sophisticated features; these promise $O(M^3)$ cost, with good performance in low dimensional tasks such as spatial modelling, but they only work with a very limited class of kernels, excluding some of the most commonly used. In this work, we propose integrated Fourier features, which extends these performance benefits to a very broad class of stationary covariance functions. We motivate the method and choice of parameters from a convergence analysis and empirical exploration, and show practical speedup in synthetic and real world spatial regression tasks.

While language models are powerful and versatile, they often fail to address highly complex problems. This is because solving complex problems requires deliberate thinking, which has been only minimally guided during training. In this paper, we propose a new method called Cumulative Reasoning (CR), which employs language models in a cumulative and iterative manner to emulate human thought processes. By decomposing tasks into smaller components, CR streamlines the problem-solving process, rendering it both more manageable and effective. For logical inference tasks, CR consistently outperforms existing methods with an improvement up to 9.3%, and achieves the astonishing accuracy of 98.04% on the curated FOLIO wiki dataset. In the context of the Game of 24, CR achieves an accuracy of 98%, which signifies a substantial enhancement of 24% over the previous state-of-the-art method. Finally, on the MATH dataset, we establish new state-of-the-art results with 58.0% overall accuracy, surpassing the previous best approach by a margin of 4.2%, and achieving 43% relative improvement on the hardest level 5 problems (22.4% to 32.1%). Code is available at //github.com/iiis-ai/cumulative-reasoning.

Triple extraction is an essential task in information extraction for natural language processing and knowledge graph construction. In this paper, we revisit the end-to-end triple extraction task for sequence generation. Since generative triple extraction may struggle to capture long-term dependencies and generate unfaithful triples, we introduce a novel model, contrastive triple extraction with a generative transformer. Specifically, we introduce a single shared transformer module for encoder-decoder-based generation. To generate faithful results, we propose a novel triplet contrastive training object. Moreover, we introduce two mechanisms to further improve model performance (i.e., batch-wise dynamic attention-masking and triple-wise calibration). Experimental results on three datasets (i.e., NYT, WebNLG, and MIE) show that our approach achieves better performance than that of baselines.

It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.

Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results. Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses. We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly. Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge.