We investigate the link between regularised self-transport problems and maximum likelihood estimation in Gaussian mixture models (GMM). This link suggests that self-transport followed by a clustering technique leads to principled estimators at a reasonable computational cost. Also, robustness, sparsity and stability properties of the optimal transport plan arguably make the regularised self-transport a statistical tool of choice for the GMM.
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Bias correction can often improve the finite sample performance of estimators. We show that the choice of bias correction method has no effect on the higher-order variance of semiparametrically efficient parametric estimators, so long as the estimate of the bias is asymptotically linear. It is also shown that bootstrap, jackknife, and analytical bias estimates are asymptotically linear for estimators with higher-order expansions of a standard form. In particular, we find that for a variety of estimators the straightforward bootstrap bias correction gives the same higher-order variance as more complicated analytical or jackknife bias corrections. In contrast, bias corrections that do not estimate the bias at the parametric rate, such as the split-sample jackknife, result in larger higher-order variances in the i.i.d. setting we focus on. For both a cross-sectional MLE and a panel model with individual fixed effects, we show that the split-sample jackknife has a higher-order variance term that is twice as large as that of the `leave-one-out' jackknife.
In the quest to advance human-centric natural language generation (NLG) systems, ensuring alignment between NLG models and human preferences is crucial. For this alignment, current popular methods leverage a reinforcement learning (RL) approach with a reward model trained on feedback from humans. However, inherent disagreements due to the subjective nature of human preferences pose a significant challenge for training the reward model, resulting in a deterioration of the NLG performance. To tackle this issue, previous approaches typically rely on majority voting or averaging to consolidate multiple inconsistent preferences into a merged one. Although straightforward to understand and execute, such methods suffer from an inability to capture the nuanced degrees of disaggregation among humans and may only represent a specialized subset of individuals, thereby lacking the ability to quantitatively disclose the universality of human preferences. To address this challenge, this paper proposes a novel approach, which employs a Bayesian framework to account for the distribution of disagreements among human preferences as training a preference model, and names it as d-PM. Besides, considering the RL strategy's inefficient and complex training process over the training efficiency, we further propose utilizing the contrastive learning strategy to train the NLG model with the preference scores derived from the d-PM model. Extensive experiments on two human-centric NLG tasks, i.e., emotional support conversation and integrity "Rule-of-Thumb" generation, show that our method consistently exceeds previous SOTA models in both automatic and human evaluations.
Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as interacting particle systems, which reveals that clusters emerge in long time. Our study explores the underlying theory and offers new perspectives for mathematicians as well as computer scientists.
Deep neural networks (DNNs) are vulnerable to backdoor attacks, where the adversary manipulates a small portion of training data such that the victim model predicts normally on the benign samples but classifies the triggered samples as the target class. The backdoor attack is an emerging yet threatening training-phase threat, leading to serious risks in DNN-based applications. In this paper, we revisit the trigger patterns of existing backdoor attacks. We reveal that they are either visible or not sparse and therefore are not stealthy enough. More importantly, it is not feasible to simply combine existing methods to design an effective sparse and invisible backdoor attack. To address this problem, we formulate the trigger generation as a bi-level optimization problem with sparsity and invisibility constraints and propose an effective method to solve it. The proposed method is dubbed sparse and invisible backdoor attack (SIBA). We conduct extensive experiments on benchmark datasets under different settings, which verify the effectiveness of our attack and its resistance to existing backdoor defenses. The codes for reproducing main experiments are available at \url{//github.com/YinghuaGao/SIBA}.
A high-order, degree-adaptive hybridizable discontinuous Galerkin (HDG) method is presented for two-fluid incompressible Stokes flows, with boundaries and interfaces described using NURBS. The NURBS curves are embedded in a fixed Cartesian grid, yielding an unfitted HDG scheme capable of treating the exact geometry of the boundaries/interfaces, circumventing the need for fitted, high-order, curved meshes. The framework of the NURBS-enhanced finite element method (NEFEM) is employed for accurate quadrature along immersed NURBS and in elements cut by NURBS curves. A Nitsche's formulation is used to enforce Dirichlet conditions on embedded surfaces, yielding unknowns only on the mesh skeleton as in standard HDG, without introducing any additional degree of freedom on non-matching boundaries/interfaces. The resulting unfitted HDG-NEFEM method combines non-conforming meshes, exact NURBS geometry and high-order approximations to provide high-fidelity results on coarse meshes, independent of the geometric features of the domain. Numerical examples illustrate the optimal accuracy and robustness of the method, even in the presence of badly cut cells or faces, and its suitability to simulate microfluidic systems from CAD geometries.
May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May's axioms, we can uniquely determine how to vote on three alternatives. In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid the so-called strong no show paradox. We prove a theorem stating that any preferential voting method satisfying our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, agrees with Minimax voting in all three-alternative elections, except perhaps in some improbable knife-edged elections in which ties may arise and be broken in different ways.
Heterogeneous graph neural networks (HGNNs) as an emerging technique have shown superior capacity of dealing with heterogeneous information network (HIN). However, most HGNNs follow a semi-supervised learning manner, which notably limits their wide use in reality since labels are usually scarce in real applications. Recently, contrastive learning, a self-supervised method, becomes one of the most exciting learning paradigms and shows great potential when there are no labels. In this paper, we study the problem of self-supervised HGNNs and propose a novel co-contrastive learning mechanism for HGNNs, named HeCo. Different from traditional contrastive learning which only focuses on contrasting positive and negative samples, HeCo employs cross-viewcontrastive mechanism. Specifically, two views of a HIN (network schema and meta-path views) are proposed to learn node embeddings, so as to capture both of local and high-order structures simultaneously. Then the cross-view contrastive learning, as well as a view mask mechanism, is proposed, which is able to extract the positive and negative embeddings from two views. This enables the two views to collaboratively supervise each other and finally learn high-level node embeddings. Moreover, two extensions of HeCo are designed to generate harder negative samples with high quality, which further boosts the performance of HeCo. Extensive experiments conducted on a variety of real-world networks show the superior performance of the proposed methods over the state-of-the-arts.
Recently pre-trained language representation models such as BERT have shown great success when fine-tuned on downstream tasks including information retrieval (IR). However, pre-training objectives tailored for ad-hoc retrieval have not been well explored. In this paper, we propose Pre-training with Representative wOrds Prediction (PROP) for ad-hoc retrieval. PROP is inspired by the classical statistical language model for IR, specifically the query likelihood model, which assumes that the query is generated as the piece of text representative of the "ideal" document. Based on this idea, we construct the representative words prediction (ROP) task for pre-training. Given an input document, we sample a pair of word sets according to the document language model, where the set with higher likelihood is deemed as more representative of the document. We then pre-train the Transformer model to predict the pairwise preference between the two word sets, jointly with the Masked Language Model (MLM) objective. By further fine-tuning on a variety of representative downstream ad-hoc retrieval tasks, PROP achieves significant improvements over baselines without pre-training or with other pre-training methods. We also show that PROP can achieve exciting performance under both the zero- and low-resource IR settings. The code and pre-trained models are available at //github.com/Albert-Ma/PROP.
Recent work pre-training Transformers with self-supervised objectives on large text corpora has shown great success when fine-tuned on downstream NLP tasks including text summarization. However, pre-training objectives tailored for abstractive text summarization have not been explored. Furthermore there is a lack of systematic evaluation across diverse domains. In this work, we propose pre-training large Transformer-based encoder-decoder models on massive text corpora with a new self-supervised objective. In PEGASUS, important sentences are removed/masked from an input document and are generated together as one output sequence from the remaining sentences, similar to an extractive summary. We evaluated our best PEGASUS model on 12 downstream summarization tasks spanning news, science, stories, instructions, emails, patents, and legislative bills. Experiments demonstrate it achieves state-of-the-art performance on all 12 downstream datasets measured by ROUGE scores. Our model also shows surprising performance on low-resource summarization, surpassing previous state-of-the-art results on 6 datasets with only 1000 examples. Finally we validated our results using human evaluation and show that our model summaries achieve human performance on multiple datasets.
Automatically creating the description of an image using any natural languages sentence like English is a very challenging task. It requires expertise of both image processing as well as natural language processing. This paper discuss about different available models for image captioning task. We have also discussed about how the advancement in the task of object recognition and machine translation has greatly improved the performance of image captioning model in recent years. In addition to that we have discussed how this model can be implemented. In the end, we have also evaluated the performance of model using standard evaluation matrices.
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