Nested simulation concerns estimating functionals of a conditional expectation via simulation. In this paper, we propose a new method based on kernel ridge regression to exploit the smoothness of the conditional expectation as a function of the multidimensional conditioning variable. Asymptotic analysis shows that the proposed method can effectively alleviate the curse of dimensionality on the convergence rate as the simulation budget increases, provided that the conditional expectation is sufficiently smooth. The smoothness bridges the gap between the cubic root convergence rate (that is, the optimal rate for the standard nested simulation) and the square root convergence rate (that is, the canonical rate for the standard Monte Carlo simulation). We demonstrate the performance of the proposed method via numerical examples from portfolio risk management and input uncertainty quantification.
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The problem of learning one task with samples from another task has received much interest recently. In this paper, we ask a fundamental question: when is combining data from two tasks better than learning one task alone? Intuitively, the transfer effect from one task to another task depends on dataset shifts such as sample sizes and covariance matrices. However, quantifying such a transfer effect is challenging since we need to compare the risks between joint learning and single-task learning, and the comparative advantage of one over the other depends on the exact kind of dataset shift between both tasks. This paper uses random matrix theory to tackle this challenge in a linear regression setting with two tasks. We give precise asymptotics about the excess risks of some commonly used estimators in the high-dimensional regime, when the sample sizes increase proportionally with the feature dimension at fixed ratios. The precise asymptotics is provided as a function of the sample sizes and covariate/model shifts, which can be used to study transfer effects: In a random-effects model, we give conditions to determine positive and negative transfers between learning two tasks versus single-task learning; the conditions reveal intricate relations between dataset shifts and transfer effects. Simulations justify the validity of the asymptotics in finite dimensions. Our analysis examines several functions of two different sample covariance matrices, revealing some estimates that generalize classical results in the random matrix theory literature, which may be of independent interest.
In this paper, we propose a novel ROM stabilization strategy for under-resolved convection-dominated flows, the approximate deconvolution Leray ROM (ADL-ROM). The new ADL-ROM introduces AD as a new means to increase the accuracy of the classical Leray ROM (L-ROM) without degrading its numerical stability. We also introduce two new AD ROM strategies: the Tikhonov and van Cittert methods. Our numerical investigation for convection-dominated systems shows that, when the filter radius is relatively large, the new ADL-ROM is more accurate than the standard L-ROM. Furthermore, the new ADL-ROM is less sensitive with respect to model parameters than L-ROM.
Activation functions are essential components of neural networks. In this paper, we introduce a new activation function called the Truncated and Signed Square Root (TSSR) function. This function is distinctive because it is odd, nonlinear, monotone and differentiable. Its gradient is continuous and always positive. Thanks to these properties, it has the potential to improve the numerical stability of neural networks. Several experiments confirm that the proposed TSSR has better performance than other stat-of-the-art activation functions. The proposed function has significant implications for the development of neural network models and can be applied to a wide range of applications in fields such as computer vision, natural language processing, and speech recognition.
Contrastive cross-modality pretraining approaches have recently exhibited impressive success in diverse fields. In this paper, we propose GEmo-CLAP, a kind of gender-attribute-enhanced contrastive language-audio pretraining (CLAP) method for speech emotion recognition (SER).Specifically, an effective emotion CLAP model (Emo-CLAP) is first built, using various self-supervised pre-trained models for SER. Second, given the significance of the gender attribute in speech emotion modeling, two novel soft label based GEmo-CLAP (SL-GEmo-CLAP) and multi-task learning based GEmo-CLAP (ML-GEmo-CLAP) are further proposed to incorporate gender information of speech signals, forming more reasonable objectives. Experiments on IEMOCAP demonstrate that our proposed two GEmo-CLAPs consistently outperform the baseline Emo-CLAP with various pre-trained models, while also achieving the best recognition performance compared with state-of-the-art SER methods. Remarkably, the proposed WavLM-based SL-GEmo-CLAP model achieves the best UAR of 81.43\% and WAR of 83.16\%.
In this paper, we consider the full Lambek calculus enriched with subexponential modalities in a distributive setting. We show that the distributive Lambek calculus with subexponentials is complete with respect to its Kripke frames via canonical extensions. In this approach, we consider subexponentials as S4-like modalities and each modality is interpreted with a reflexive and transitive relation similarly to usual Kripke semantics.
Link prediction is a very fundamental task on graphs. Inspired by traditional path-based methods, in this paper we propose a general and flexible representation learning framework based on paths for link prediction. Specifically, we define the representation of a pair of nodes as the generalized sum of all path representations, with each path representation as the generalized product of the edge representations in the path. Motivated by the Bellman-Ford algorithm for solving the shortest path problem, we show that the proposed path formulation can be efficiently solved by the generalized Bellman-Ford algorithm. To further improve the capacity of the path formulation, we propose the Neural Bellman-Ford Network (NBFNet), a general graph neural network framework that solves the path formulation with learned operators in the generalized Bellman-Ford algorithm. The NBFNet parameterizes the generalized Bellman-Ford algorithm with 3 neural components, namely INDICATOR, MESSAGE and AGGREGATE functions, which corresponds to the boundary condition, multiplication operator, and summation operator respectively. The NBFNet is very general, covers many traditional path-based methods, and can be applied to both homogeneous graphs and multi-relational graphs (e.g., knowledge graphs) in both transductive and inductive settings. Experiments on both homogeneous graphs and knowledge graphs show that the proposed NBFNet outperforms existing methods by a large margin in both transductive and inductive settings, achieving new state-of-the-art results.
Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive capacity and effective model complexity. We review the existing studies on those two categories along four important factors, including model framework, model size, optimization process and data complexity. We also discuss the applications of deep learning model complexity including understanding model generalization capability, model optimization, and model selection and design. We conclude by proposing several interesting future directions.
In this paper, we present a comprehensive review of the imbalance problems in object detection. To analyze the problems in a systematic manner, we introduce a problem-based taxonomy. Following this taxonomy, we discuss each problem in depth and present a unifying yet critical perspective on the solutions in the literature. In addition, we identify major open issues regarding the existing imbalance problems as well as imbalance problems that have not been discussed before. Moreover, in order to keep our review up to date, we provide an accompanying webpage which catalogs papers addressing imbalance problems, according to our problem-based taxonomy. Researchers can track newer studies on this webpage available at: //github.com/kemaloksuz/ObjectDetectionImbalance .
In this paper, we proposed to apply meta learning approach for low-resource automatic speech recognition (ASR). We formulated ASR for different languages as different tasks, and meta-learned the initialization parameters from many pretraining languages to achieve fast adaptation on unseen target language, via recently proposed model-agnostic meta learning algorithm (MAML). We evaluated the proposed approach using six languages as pretraining tasks and four languages as target tasks. Preliminary results showed that the proposed method, MetaASR, significantly outperforms the state-of-the-art multitask pretraining approach on all target languages with different combinations of pretraining languages. In addition, since MAML's model-agnostic property, this paper also opens new research direction of applying meta learning to more speech-related applications.
Salient object detection is a problem that has been considered in detail and many solutions proposed. In this paper, we argue that work to date has addressed a problem that is relatively ill-posed. Specifically, there is not universal agreement about what constitutes a salient object when multiple observers are queried. This implies that some objects are more likely to be judged salient than others, and implies a relative rank exists on salient objects. The solution presented in this paper solves this more general problem that considers relative rank, and we propose data and metrics suitable to measuring success in a relative objects saliency landscape. A novel deep learning solution is proposed based on a hierarchical representation of relative saliency and stage-wise refinement. We also show that the problem of salient object subitizing can be addressed with the same network, and our approach exceeds performance of any prior work across all metrics considered (both traditional and newly proposed).
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