We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an unbiased estimator and that one must time-discretize the diffusion process. In such scenarios it has been shown how one can introduce the multilevel Monte Carlo method to reduce the cost to compute posterior expected values of the parameters for a pre-specified mean square error (MSE). These afore-mentioned methods rely on upon the Euler-Maruyama discretization scheme which is well-known in numerical analysis to have slow convergence properties. We adapt stochastic Runge-Kutta (SRK) methods for Bayesian parameter estimation of static parameters for diffusions. This can be implemented in high-dimensions of the diffusion and seemingly under-appreciated in the uncertainty quantification and statistics fields. For a class of diffusions and SRK methods, we consider the estimation of the posterior expectation of the parameters. We prove that to achieve a MSE of $\mathcal{O}(\epsilon^2)$, for $\epsilon>0$ given, the associated work is $\mathcal{O}(\epsilon^{-2})$. Whilst the latter is achievable for the Milstein scheme, this method is often not applicable for diffusions in dimension larger than two. We also illustrate our methodology in several numerical examples.
Recent advances in Transformer architectures have empowered their empirical success in a variety of tasks across different domains. However, existing works mainly focus on predictive accuracy and computational cost, without considering other practical issues, such as robustness to contaminated samples. Recent work by Nguyen et al., (2022) has shown that the self-attention mechanism, which is the center of the Transformer architecture, can be viewed as a non-parametric estimator based on kernel density estimation (KDE). This motivates us to leverage a set of robust kernel density estimation methods for alleviating the issue of data contamination. Specifically, we introduce a series of self-attention mechanisms that can be incorporated into different Transformer architectures and discuss the special properties of each method. We then perform extensive empirical studies on language modeling and image classification tasks. Our methods demonstrate robust performance in multiple scenarios while maintaining competitive results on clean datasets.
Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the literature with widely varying performance, and the problem of selecting suitable encodings for a given problem instance is not trivial. We explore the problem of selecting encodings for pseudo-Boolean and linear constraints using a supervised machine learning approach. We show that it is possible to select encodings effectively using a standard set of features for constraint problems; however we obtain better performance with a new set of features specifically designed for the pseudo-Boolean and linear constraints. In fact, we achieve good results when selecting encodings for unseen problem classes. Our results compare favourably to AutoFolio when using the same feature set. We discuss the relative importance of instance features to the task of selecting the best encodings, and compare several variations of the machine learning method.
Emotion recognition is a crucial task for human conversation understanding. It becomes more challenging with the notion of multimodal data, e.g., language, voice, and facial expressions. As a typical solution, the global- and the local context information are exploited to predict the emotional label for every single sentence, i.e., utterance, in the dialogue. Specifically, the global representation could be captured via modeling of cross-modal interactions at the conversation level. The local one is often inferred using the temporal information of speakers or emotional shifts, which neglects vital factors at the utterance level. Additionally, most existing approaches take fused features of multiple modalities in an unified input without leveraging modality-specific representations. Motivating from these problems, we propose the Relational Temporal Graph Neural Network with Auxiliary Cross-Modality Interaction (CORECT), an novel neural network framework that effectively captures conversation-level cross-modality interactions and utterance-level temporal dependencies with the modality-specific manner for conversation understanding. Extensive experiments demonstrate the effectiveness of CORECT via its state-of-the-art results on the IEMOCAP and CMU-MOSEI datasets for the multimodal ERC task.
Despite recent attention and exploration of depth for various tasks, it is still an unexplored modality for weakly-supervised object detection (WSOD). We propose an amplifier method for enhancing the performance of WSOD by integrating depth information. Our approach can be applied to any WSOD method based on multiple-instance learning, without necessitating additional annotations or inducing large computational expenses. Our proposed method employs a monocular depth estimation technique to obtain hallucinated depth information, which is then incorporated into a Siamese WSOD network using contrastive loss and fusion. By analyzing the relationship between language context and depth, we calculate depth priors to identify the bounding box proposals that may contain an object of interest. These depth priors are then utilized to update the list of pseudo ground-truth boxes, or adjust the confidence of per-box predictions. Our proposed method is evaluated on six datasets (COCO, PASCAL VOC, Conceptual Captions, Clipart1k, Watercolor2k, and Comic2k) by implementing it on top of two state-of-the-art WSOD methods, and we demonstrate a substantial enhancement in performance.
The dominant paradigm in 3D human pose estimation that lifts a 2D pose sequence to 3D heavily relies on long-term temporal clues (i.e., using a daunting number of video frames) for improved accuracy, which incurs performance saturation, intractable computation and the non-causal problem. This can be attributed to their inherent inability to perceive spatial context as plain 2D joint coordinates carry no visual cues. To address this issue, we propose a straightforward yet powerful solution: leveraging the readily available intermediate visual representations produced by off-the-shelf (pre-trained) 2D pose detectors -- no finetuning on the 3D task is even needed. The key observation is that, while the pose detector learns to localize 2D joints, such representations (e.g., feature maps) implicitly encode the joint-centric spatial context thanks to the regional operations in backbone networks. We design a simple baseline named Context-Aware PoseFormer to showcase its effectiveness. Without access to any temporal information, the proposed method significantly outperforms its context-agnostic counterpart, PoseFormer, and other state-of-the-art methods using up to hundreds of video frames regarding both speed and precision. Project page: //qitaozhao.github.io/ContextAware-PoseFormer
We present an efficient framework for solving constrained global non-convex polynomial optimization problems. We prove the existence of an equivalent nonlinear reformulation of such problems that possesses essentially no spurious local minima. We show through numerical experiments that polynomial scaling in dimension and degree is achievable for computing the optimal value and location of previously intractable global constrained polynomial optimization problems in high dimension.
Emotion recognition in conversation (ERC) aims to detect the emotion label for each utterance. Motivated by recent studies which have proven that feeding training examples in a meaningful order rather than considering them randomly can boost the performance of models, we propose an ERC-oriented hybrid curriculum learning framework. Our framework consists of two curricula: (1) conversation-level curriculum (CC); and (2) utterance-level curriculum (UC). In CC, we construct a difficulty measurer based on "emotion shift" frequency within a conversation, then the conversations are scheduled in an "easy to hard" schema according to the difficulty score returned by the difficulty measurer. For UC, it is implemented from an emotion-similarity perspective, which progressively strengthens the model's ability in identifying the confusing emotions. With the proposed model-agnostic hybrid curriculum learning strategy, we observe significant performance boosts over a wide range of existing ERC models and we are able to achieve new state-of-the-art results on four public ERC datasets.
Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.
Named entity recognition (NER) is the task to identify text spans that mention named entities, and to classify them into predefined categories such as person, location, organization etc. NER serves as the basis for a variety of natural language applications such as question answering, text summarization, and machine translation. Although early NER systems are successful in producing decent recognition accuracy, they often require much human effort in carefully designing rules or features. In recent years, deep learning, empowered by continuous real-valued vector representations and semantic composition through nonlinear processing, has been employed in NER systems, yielding stat-of-the-art performance. In this paper, we provide a comprehensive review on existing deep learning techniques for NER. We first introduce NER resources, including tagged NER corpora and off-the-shelf NER tools. Then, we systematically categorize existing works based on a taxonomy along three axes: distributed representations for input, context encoder, and tag decoder. Next, we survey the most representative methods for recent applied techniques of deep learning in new NER problem settings and applications. Finally, we present readers with the challenges faced by NER systems and outline future directions in this area.
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.