In robust optimization problems, the magnitude of perturbations is relatively small. Consequently, solutions within certain regions are less likely to represent the robust optima when perturbations are introduced. Hence, a more efficient search process would benefit from increased opportunities to explore promising regions where global optima or good local optima are situated. In this paper, we introduce a novel robust evolutionary algorithm named the dual-stage robust evolutionary algorithm (DREA) aimed at discovering robust solutions. DREA operates in two stages: the peak-detection stage and the robust solution-searching stage. The primary objective of the peak-detection stage is to identify peaks in the fitness landscape of the original optimization problem. Conversely, the robust solution-searching stage focuses on swiftly identifying the robust optimal solution using information obtained from the peaks discovered in the initial stage. These two stages collectively enable the proposed DREA to efficiently obtain the robust optimal solution for the optimization problem. This approach achieves a balance between solution optimality and robustness by separating the search processes for optimal and robust optimal solutions. Experimental results demonstrate that DREA significantly outperforms five state-of-the-art algorithms across 18 test problems characterized by diverse complexities. Moreover, when evaluated on higher-dimensional robust optimization problems (100-$D$ and 200-$D$), DREA also demonstrates superior performance compared to all five counterpart algorithms.
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Structured sparsity is an efficient way to prune the complexity of modern Machine Learning (ML) applications and to simplify the handling of sparse data in hardware. In such cases, the acceleration of structured-sparse ML models is handled by sparse systolic tensor arrays. The increasing prevalence of ML in safety-critical systems requires enhancing the sparse tensor arrays with online error detection for managing random hardware failures. Algorithm-based fault tolerance has been proposed as a low-cost mechanism to check online the result of computations against random hardware failures. In this work, we address a key architectural challenge with structured-sparse tensor arrays: how to provide online error checking for a range of structured sparsity levels while maintaining high utilization of the hardware. Experimental results highlight the minimum hardware overhead incurred by the proposed checking logic and its error detection properties after injecting random hardware faults on sparse tensor arrays that execute layers of ResNet50 CNN.
This paper studies the problem of shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we consider the model $y = \Pi_* X \beta_* + w$, where $X$ is an $n \times d$ standard Gaussian design matrix, $w$ is Gaussian noise with entrywise variance $\sigma^2$, $\Pi_*$ is an unknown $n \times n$ permutation matrix, and $\beta_*$ is the regression coefficient, also unknown. Previous work has shown that, in the large $n$-limit, the minimal signal-to-noise ratio ($\mathsf{SNR}$), $\lVert \beta_* \rVert^2/\sigma^2$, for recovering the unknown permutation exactly with high probability is between $n^2$ and $n^C$ for some absolute constant $C$ and the sharp threshold is unknown even for $d=1$. We show that this threshold is precisely $\mathsf{SNR} = n^4$ for exact recovery throughout the sublinear regime $d=o(n)$. As a by-product of our analysis, we also determine the sharp threshold of almost exact recovery to be $\mathsf{SNR} = n^2$, where all but a vanishing fraction of the permutation is reconstructed.
Precise modeling soft robots remains a challenge due to their infinite-dimensional nature governed by partial differential equations. This paper introduces an innovative approach for modeling soft pneumatic actuators, employing a nonlinear framework through data-driven parameter estimation. The research begins by introducing Ludwick's Law, providing a accurate representation of the large deflections exhibited by soft materials. Three key material properties, namely Young's modulus, tensile stress, and mixed viscosity, are utilized to estimate the parameters inside the nonlinear model using the least squares method. Subsequently, a nonlinear dynamic model for soft actuators is constructed by applying Ludwick's Law. To validate the accuracy and effectiveness of the proposed method, several experiments are performed demonstrating the model's capabilities in predicting the dynamic behavior of soft pneumatic actuators. In conclusion, this work contributes to the advancement of soft pneumatic actuator modeling that represents their nonlinear behavior.
Several applications in time series forecasting require predicting multiple steps ahead. Despite the vast amount of literature in the topic, both classical and recent deep learning based approaches have mostly focused on minimising performance averaged over the predicted window. We observe that this can lead to disparate distributions of errors across forecasting steps, especially for recent transformer architectures trained on popular forecasting benchmarks. That is, optimising performance on average can lead to undesirably large errors at specific time-steps. In this work, we present a Constrained Learning approach for long-term time series forecasting that aims to find the best model in terms of average performance that respects a user-defined upper bound on the loss at each time-step. We call our approach loss shaping constraints because it imposes constraints on the loss at each time step, and leverage recent duality results to show that despite its non-convexity, the resulting problem has a bounded duality gap. We propose a practical Primal-Dual algorithm to tackle it, and demonstrate that the proposed approach exhibits competitive average performance in time series forecasting benchmarks, while shaping the distribution of errors across the predicted window.
Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or discrete, including in high-dimensions. However, in many applications data span variables of different types (e.g. continuous, count, binary, ordinal, etc.), whose principled joint analysis is nontrivial. Latent Gaussian copula models, in which all variables are modeled as transformations of underlying jointly Gaussian variables, represent a useful approach. Recent advances have shown how the binary-continuous case can be tackled, but the general mixed variable type regime remains challenging. In this work, we make the simple yet useful observation that classical ideas concerning polychoric and polyserial correlations can be leveraged in a latent Gaussian copula framework. Building on this observation we propose flexible and scalable methodology for data with variables of entirely general mixed type. We study the key properties of the approaches theoretically and empirically, via extensive simulations as well an illustrative application to data from the UK Biobank concerning COVID-19 risk factors.
We introduce a multivariate local-linear estimator for multivariate regression discontinuity designs in which treatment is assigned by crossing a boundary in the space of running variables. The dominant approach uses the Euclidean distance from a boundary point as the scalar running variable; hence, multivariate designs are handled as uni-variate designs. However, the distance running variable is incompatible with the assumption for asymptotic validity. We handle multivariate designs as multivariate. In this study, we develop a novel asymptotic normality for multivariate local-polynomial estimators. Our estimator is asymptotically valid and can capture heterogeneous treatment effects over the boundary. We demonstrate the effectiveness of our estimator through numerical simulations. Our empirical illustration of a Colombian scholarship study reveals a richer heterogeneity (including its absence) of the treatment effect that is hidden in the original estimates.
Given the significance of speech emotion recognition, numerous methods have been developed in recent years to create effective and efficient systems in this domain. One of these methods involves the use of pretrained transformers, fine-tuned to address this specific problem, resulting in high accuracy. Despite extensive discussions and global-scale efforts to enhance these systems, the application of this innovative and effective approach has received less attention in the context of Persian speech emotion recognition. In this article, we review the field of speech emotion recognition and its background, with an emphasis on the importance of employing transformers in this context. We present two models, one based on spectrograms and the other on the audio itself, fine-tuned using the shEMO dataset. These models significantly enhance the accuracy of previous systems, increasing it from approximately 65% to 80% on the mentioned dataset. Subsequently, to investigate the effect of multilinguality on the fine-tuning process, these same models are fine-tuned twice. First, they are fine-tuned using the English IEMOCAP dataset, and then they are fine-tuned with the Persian shEMO dataset. This results in an improved accuracy of 82% for the Persian emotion recognition system. Keywords: Persian Speech Emotion Recognition, shEMO, Self-Supervised Learning
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.
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, thereby allowing manual manipulation in predicting the final answer.
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