In data-driven optimization, sample average approximation (SAA) is known to suffer from the so-called optimizer's curse that causes an over-optimistic evaluation of the solution performance. We argue that a special type of distributionallly robust optimization (DRO) formulation offers theoretical advantages in correcting for this optimizer's curse compared to simple ``margin'' adjustments to SAA and other DRO approaches: It attains a statistical bound on the out-of-sample performance, for a wide class of objective functions and distributions, that is nearly tightest in terms of exponential decay rate. This DRO uses an ambiguity set based on a Kullback Leibler (KL) divergence smoothed by the Wasserstein or L\'evy-Prokhorov (LP) distance via a suitable distance optimization. Computationally, we also show that such a DRO, and its generalized versions using smoothed $f$-divergence, are not harder than DRO problems based on $f$-divergence or Wasserstein distances, rendering our DRO formulations both statistically optimal and computationally viable.
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Structural clustering is one of the most popular graph clustering methods, which has achieved great performance improvement by utilizing GPUs. Even though, the state-of-the-art GPU-based structural clustering algorithm, GPUSCAN, still suffers from efficiency issues since lots of extra costs are introduced for parallelization. Moreover, GPUSCAN assumes that the graph is resident in the GPU memory. However, the GPU memory capacity is limited currently while many real-world graphs are big and cannot fit in the GPU memory, which makes GPUSCAN unable to handle large graphs. Motivated by this, we present a new GPU-based structural clustering algorithm, GPUSCAN++, in this paper. To address the efficiency issue, we propose a new progressive clustering method tailored for GPUs that not only avoid high parallelization costs but also fully exploits the computing resources of GPUs. To address the GPU memory limitation issue, we propose a partition-based algorithm for structural clustering that can process large graphs with limited GPU memory. We conduct experiments on real graphs, and the experimental results demonstrate that our algorithm can achieve up to 168 times speedup compared with the state-of-the-art GPU-based algorithm when the graph can be resident in the GPU memory. Moreover, our algorithm is scalable to handle large graphs. As an example, our algorithm can finish the structural clustering on a graph with 1.8 billion edges using less than 2 GB GPU memory.
We propose a diarization system, that estimates "who spoke when" based on spatial information, to be used as a front-end of a meeting transcription system running on the signals gathered from an acoustic sensor network (ASN). Although the spatial distribution of the microphones is advantageous, exploiting the spatial diversity for diarization and signal enhancement is challenging, because the microphones' positions are typically unknown, and the recorded signals are initially unsynchronized in general. Here, we approach these issues by first blindly synchronizing the signals and then estimating time differences of arrival (TDOAs). The TDOA information is exploited to estimate the speakers' activity, even in the presence of multiple speakers being simultaneously active. This speaker activity information serves as a guide for a spatial mixture model, on which basis the individual speaker's signals are extracted via beamforming. Finally, the extracted signals are forwarded to a speech recognizer. Additionally, a novel initialization scheme for spatial mixture models based on the TDOA estimates is proposed. Experiments conducted on real recordings from the LibriWASN data set have shown that our proposed system is advantageous compared to a system using a spatial mixture model, which does not make use of external diarization information.
On dedicated analog hardware, equilibrium propagation is an energy-efficient alternative to backpropagation. In spite of its theoretical guarantees, its application in the AI domain remains limited to the discriminative setting. Meanwhile, despite its high computational demands, generative AI is on the rise. In this paper, we demonstrate the application of Equilibrium Propagation in training a variational autoencoder (VAE) for generative modeling. Leveraging the symmetric nature of Hopfield networks, we propose using a single model to serve as both the encoder and decoder which could effectively halve the required chip size for VAE implementations, paving the way for more efficient analog hardware configurations.
Given a finite set of unknown distributions or arms that can be sampled, we consider the problem of identifying the one with the maximum mean using a $\delta$-correct algorithm (an adaptive, sequential algorithm that restricts the probability of error to a specified $\delta$) that has minimum sample complexity. Lower bounds for $\delta$-correct algorithms are well known. $\delta$-correct algorithms that match the lower bound asymptotically as $\delta$ reduces to zero have been previously developed when arm distributions are restricted to a single parameter exponential family. In this paper, we first observe a negative result that some restrictions are essential, as otherwise, under a $\delta$-correct algorithm, distributions with unbounded support would require an infinite number of samples in expectation. We then propose a $\delta$-correct algorithm that matches the lower bound as $\delta$ reduces to zero under the mild restriction that a known bound on the expectation of $(1+\epsilon)^{th}$ moment of the underlying random variables exists, for $\epsilon > 0$. We also propose batch processing and identify near-optimal batch sizes to speed up the proposed algorithm substantially. The best-arm problem has many learning applications, including recommendation systems and product selection. It is also a well-studied classic problem in the simulation community.
In this work, the development of a framework for the multi-scale data-driven parametrization of averaged-scale models is outlined and applied to dispersive transport. Dispersive transport is a common phenomena included in transport models at the averaged scale, describing the velocity and geometry dependent mixing seen at the pore scale. Optimal parameters for the development of dispersion tensors can be extracted from pore-scale simulations in the form of an averaged velocity and characteristic length scales. In this work, the determination of these parameters is outlined and tested first on simple and later on complex random pore geometries. These parametrizations are then used to develop a data-driven model extracting optimal parameters from pore geometries. In order to better understand the relationships between these parameters and pore geometries, we introduce a series of metrics based on interfacial geometry, volume ratios, and connectivity. These metrics are then compared against the parametrizations, and used to develop a metrics based data-driven model.
Recently, numerous tensor SVD (t-SVD)-based tensor recovery methods have emerged, showing promise in processing visual data. However, these methods often suffer from performance degradation when confronted with high-order tensor data exhibiting non-smooth changes, commonly observed in real-world scenarios but ignored by the traditional t-SVD-based methods. Our objective in this study is to provide an effective tensor recovery technique for handling non-smooth changes in tensor data and efficiently explore the correlations of high-order tensor data across its various dimensions without introducing numerous variables and weights. To this end, we introduce a new tensor decomposition and a new tensor norm called the Tensor $U_1$ norm. We utilize these novel techniques in solving the problem of high-order tensor completion problem and provide theoretical guarantees for the exact recovery of the resulting tensor completion models. An optimization algorithm is proposed to solve the resulting tensor completion model iteratively by combining the proximal algorithm with the Alternating Direction Method of Multipliers. Theoretical analysis showed the convergence of the algorithm to the Karush-Kuhn-Tucker (KKT) point of the optimization problem. Numerical experiments demonstrated the effectiveness of the proposed method in high-order tensor completion, especially for tensor data with non-smooth changes.
$k$-clique listing is a vital graph mining operator with diverse applications in various networks. The state-of-the-art algorithms all adopt a branch-and-bound (BB) framework with a vertex-oriented branching strategy (called VBBkC), which forms a sub-branch by expanding a partial $k$-clique with a vertex. These algorithms have the time complexity of $O(k m (\delta/2)^{k-2})$, where $m$ is the number of edges in the graph and $\delta$ is the degeneracy of the graph. In this paper, we propose a BB framework with a new edge-oriented branching (called EBBkC), which forms a sub-branch by expanding a partial $k$-clique with two vertices that connect each other (which correspond to an edge). We explore various edge orderings for EBBkC such that it achieves a time complexity of $O(\delta m + k m (\tau/2)^{k-2})$, where $\tau$ is an integer related to the maximum truss number of the graph and we have $\tau < \delta$. The time complexity of EBBkC is better than that of VBBkC algorithms for $k>3$ since both $O(\delta m)$ and $O(k m (\tau/2)^{k-2})$ are bounded by $O(k m (\delta/2)^{k-2})$. Furthermore, we develop specialized algorithms for sub-branches on dense graphs so that we can early-terminate them and apply the specialized algorithms. We conduct extensive experiments on 19 real graphs, and the results show that our newly developed EBBkC-based algorithms with the early termination technique consistently and largely outperform the state-of-the-art (VBBkC-based) algorithms.
The development of unmanned aerial vehicles (UAVs) has been gaining momentum in recent years owing to technological advances and a significant reduction in their cost. UAV technology can be used in a wide range of domains, including communication, agriculture, security, and transportation. It may be useful to group the UAVs into clusters/flocks in certain domains, and various challenges associated with UAV usage can be alleviated by clustering. Several computational challenges arise in UAV flock management, which can be solved by using machine learning (ML) methods. In this survey, we describe the basic terms relating to UAVS and modern ML methods, and we provide an overview of related tutorials and surveys. We subsequently consider the different challenges that appear in UAV flocks. For each issue, we survey several machine learning-based methods that have been suggested in the literature to handle the associated challenges. Thereafter, we describe various open issues in which ML can be applied to solve the different challenges of flocks, and we suggest means of using ML methods for this purpose. This comprehensive review may be useful for both researchers and developers in providing a wide view of various aspects of state-of-the-art ML technologies that are applicable to flock management.
The key challenge of image manipulation detection is how to learn generalizable features that are sensitive to manipulations in novel data, whilst specific to prevent false alarms on authentic images. Current research emphasizes the sensitivity, with the specificity overlooked. In this paper we address both aspects by multi-view feature learning and multi-scale supervision. By exploiting noise distribution and boundary artifact surrounding tampered regions, the former aims to learn semantic-agnostic and thus more generalizable features. The latter allows us to learn from authentic images which are nontrivial to be taken into account by current semantic segmentation network based methods. Our thoughts are realized by a new network which we term MVSS-Net. Extensive experiments on five benchmark sets justify the viability of MVSS-Net for both pixel-level and image-level manipulation detection.
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.
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