We consider the problem of co-optimized energy-reserve market clearing with state-of-charge (SoC) dependent bids from battery storage participants. While SoC-dependent bidding accurately captures storage's degradation and opportunity costs, such bids result in a non-convex optimization in the market clearing process. More challenging is the regulation reserve capacity clearing, where the SoC-dependent cost is uncertain as it depends on the unknown regulation trajectories ex-post of the market clearing. Addressing the nonconvexity and uncertainty in a multi-interval co-optimized real-time energy-reserve market, we introduce a simple restriction on the SoC-dependent bids along with a robust optimization formulation, transforming the non-convex market clearing under uncertainty into a standard convex piece-wise linear program and making it possible for large-scale storage integration. Under reasonable assumptions, we show that SoC-dependent bids yield higher profit for storage participants than that from SoC-independent bids. Numerical simulations demonstrate a 28%-150% profit increase of the proposed SoC-dependent bids compared with the SoC-independent counterpart.
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Though numerous solvers have been proposed for the MaxSAT problem, and the benchmark environment such as MaxSAT Evaluations provides a platform for the comparison of the state-of-the-art solvers, existing assessments were usually evaluated based on the quality, e.g., fitness, of the best-found solutions obtained within a given running time budget. However, concerning solely the final obtained solutions regarding specific time budgets may restrict us from comprehending the behavior of the solvers along the convergence process. This paper demonstrates that Empirical Cumulative Distribution Functions can be used to compare MaxSAT local search solvers' anytime performance across multiple problem instances and various time budgets. The assessment reveals distinctions in solvers' performance and displays that the (dis)advantages of solvers adjust along different running times. This work also exhibits that the quantitative and high variance assessment of anytime performance can guide machines, i.e., automatic configurators, to search for better parameter settings. Our experimental results show that the hyperparameter optimization tool, i.e., SMAC, generally achieves better parameter settings of local search when using the anytime performance as the cost function, compared to using the fitness of the best-found solutions.
In this paper, we propose a class of nonlocal models to approximate the Poisson model on manifolds with homogeneous Neumann boundary condition, where the manifolds are assumed to be embedded in high dimensional Euclid spaces. In comparison to the existing nonlocal approximation of Poisson models with Neumann boundary, we optimize the truncation error of model by adding an augmented term along the $2\delta$ layer of boundary, with $2\delta$ be the nonlocal interaction horizon. Such term is formulated by the integration of the second order normal derivative of solution through the boundary, while the second order normal derivative is expressed as the difference between the interior Laplacian and the boundary Laplacian. The concentration of our paper is on the construction of nonlocal model, the well-posedness of model, and its second-order convergence rate to its local counterpart. The localization rate of our nonlocal model is currently optimal among all related works even for the case of high dimensional Euclid spaces.
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic variable screening with random projection tools as a viable approach. More specifically, we introduce a new data-driven random projection tailored to the problem at hand and derive a theoretical bound on the gain in expected prediction error over conventional random projections. The variables to enter the projection are screened by accounting for predictor correlation. To reduce the dependence on fine-tuning choices, we aggregate over an ensemble of linear models. A thresholding parameter is introduced to obtain a higher degree of sparsity. Both this parameter and the number of models in the ensemble can be chosen by cross-validation. In extensive simulations, we compare the proposed method with other random projection tools and with classical sparse and dense methods and show that it is competitive in terms of prediction across a variety of scenarios with different sparsity and predictor covariance settings. We also show that the method with cross-validation is able to rank the variables satisfactorily. Finally, we showcase the method on two real data applications.
We consider estimating a matrix from noisy observations coming from an arbitrary additive bi- rotational invariant perturbation. We propose an estimator which is optimal among the class of rectangular rotational invariant estimators and can be applied irrespective of the prior on the signal. For the particular case of Gaussian noise, we prove the optimality of the proposed estimator, and we find an explicit expression for the MMSE in terms of the limiting singular value distribution of the observation matrix. Moreover, we prove a formula linking the asymptotic mutual information and the limit of a log-spherical integral of rectangular matrices. We also provide numerical checks for our results for general bi-rotational invariant noise, as well as Gaussian noise, which match our theoretical predictions.
Few-shot knowledge graph completion (FKGC) aims to query the unseen facts of a relation given its few-shot reference entity pairs. The side effect of noises due to the uncertainty of entities and triples may limit the few-shot learning, but existing FKGC works neglect such uncertainty, which leads them more susceptible to limited reference samples with noises. In this paper, we propose a novel uncertainty-aware few-shot KG completion framework (UFKGC) to model uncertainty for a better understanding of the limited data by learning representations under Gaussian distribution. Uncertainty representation is first designed for estimating the uncertainty scope of the entity pairs after transferring feature representations into a Gaussian distribution. Further, to better integrate the neighbors with uncertainty characteristics for entity features, we design an uncertainty-aware relational graph neural network (UR-GNN) to conduct convolution operations between the Gaussian distributions. Then, multiple random samplings are conducted for reference triples within the Gaussian distribution to generate smooth reference representations during the optimization. The final completion score for each query instance is measured by the designed uncertainty optimization to make our approach more robust to the noises in few-shot scenarios. Experimental results show that our approach achieves excellent performance on two benchmark datasets compared to its competitors.
The pursuit of accurate 3D hand pose estimation stands as a keystone for understanding human activity in the realm of egocentric vision. The majority of existing estimation methods still rely on single-view images as input, leading to potential limitations, e.g., limited field-of-view and ambiguity in depth. To address these problems, adding another camera to better capture the shape of hands is a practical direction. However, existing multi-view hand pose estimation methods suffer from two main drawbacks: 1) Requiring multi-view annotations for training, which are expensive. 2) During testing, the model becomes inapplicable if camera parameters/layout are not the same as those used in training. In this paper, we propose a novel Single-to-Dual-view adaptation (S2DHand) solution that adapts a pre-trained single-view estimator to dual views. Compared with existing multi-view training methods, 1) our adaptation process is unsupervised, eliminating the need for multi-view annotation. 2) Moreover, our method can handle arbitrary dual-view pairs with unknown camera parameters, making the model applicable to diverse camera settings. Specifically, S2DHand is built on certain stereo constraints, including pair-wise cross-view consensus and invariance of transformation between both views. These two stereo constraints are used in a complementary manner to generate pseudo-labels, allowing reliable adaptation. Evaluation results reveal that S2DHand achieves significant improvements on arbitrary camera pairs under both in-dataset and cross-dataset settings, and outperforms existing adaptation methods with leading performance. Project page: //github.com/MickeyLLG/S2DHand.
We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are characterized by an equivalent Gaussian model with an effective prior, whose parameters are entirely determined by an expansion of the non-linear function. In particular, we show that to reconstruct the signal accurately, one requires a signal-to-noise ratio growing as $N^{\frac 12 (1-1/k_F)}$, where $k_F$ is the first non-zero Fisher information coefficient of the function. We provide asymptotic characterization for the minimal achievable mean squared error (MMSE) and an approximate message-passing algorithm that reaches the MMSE under conditions analogous to the linear version of the problem. We also provide asymptotic errors achieved by methods such as principal component analysis combined with Bayesian denoising, and compare them with Bayes-optimal MMSE.
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.
Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that incorporates features from multiple scales. Initially, a foreground mask in a video frame is segmented into multi-scale superpixels. Then the human-like regions in the segmented area are identified by matching a set of extracted features from superpixels against learned features in a codebook. A carried object probability map is generated using the complement of the matching probabilities of superpixels to human-like regions and background information. A group of superpixels with high carried object probability and strong edge support is then merged to obtain the shape of the carried object. We applied our method to two challenging datasets, and results show that our method is competitive with or better than the state-of-the-art.
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