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We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the natural parameters are appropriately bounded. While the traditional maximum likelihood estimator for this class of exponential family is consistent, asymptotically normal, and asymptotically efficient, evaluating it is computationally hard. In this work, we propose a novel loss function and a computationally efficient estimator that is consistent as well as asymptotically normal under mild conditions. We show that, at the population level, our method can be viewed as the maximum likelihood estimation of a re-parameterized distribution belonging to the same class of exponential family. Further, we show that our estimator can be interpreted as a solution to minimizing a particular Bregman score as well as an instance of minimizing the \textit{surrogate} likelihood. We also provide finite sample guarantees to achieve an error (in $\ell_2$-norm) of $\alpha$ in the parameter estimation with sample complexity $O({\sf poly}(k)/\alpha^2)$. Our method achives the order-optimal sample complexity of $O({\sf log}(k)/\alpha^2)$ when tailored for node-wise-sparse Markov random fields. Finally, we demonstrate the performance of our estimator via numerical experiments.

This paper proposes Asynchronous Triggered Gradient Tracking, i.e., a distributed optimization algorithm to solve consensus optimization over networks with asynchronous communication. As a building block, we devise the continuous-time counterpart of the recently proposed (discrete-time) distributed gradient tracking called Continuous Gradient Tracking. By using a Lyapunov approach, we prove exponential stability of the equilibrium corresponding to agents' estimates being consensual to the optimal solution, with arbitrary initialization of the local estimates. Then, we propose two triggered versions of the algorithm. In the first one, the agents continuously integrate their local dynamics and exchange with neighbors their current local variables in a synchronous way. In Asynchronous Triggered Gradient Tracking, we propose a totally asynchronous scheme in which each agent sends to neighbors its current local variables based on a triggering condition that depends on a locally verifiable condition. The triggering protocol preserves the linear convergence of the algorithm and avoids the Zeno behavior, i.e., an infinite number of triggering events over a finite interval of time is excluded. By using the stability analysis of Continuous Gradient Tracking as a preparatory result, we show exponential stability of the equilibrium point holds for both triggered algorithms and any estimate initialization. Finally, the simulations validate the effectiveness of the proposed methods on a data analytics problem, showing also improved performance in terms of inter-agent communication.

We present a version of the matrix-tree theorem, which relates the determinant of a matrix to sums of weights of arborescences of its directed graph representation. Our treatment allows for non-zero column sums in the parent matrix by adding a root vertex to the usually considered matrix directed graph. We use our result to prove a version of the matrix-forest, or all-minors, theorem, which relates minors of the matrix to forests of arborescences of the matrix digraph. We then show that it is possible, when the source and target vertices of an arc are not strongly connected, to move the source of the arc in the matrix directed graph and leave the resulting matrix determinant unchanged, as long as the source and target vertices are not strongly connected after the move. This result enables graphical strategies for factoring matrix determinants.

This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von K\'{a}rm\'{a}n equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete solution to the non-linear problem is discussed. A priori error estimate in the energy norm is established under minimal regularity assumptions on the exact solution. Error estimates in piecewise $H^1$ and $L^2$ norm are also derived. A working procedure to find an approximation for the discrete solution using Newtons method is discussed. Numerical results that justify theoretical estimates are presented.

A well-known approach in the design of efficient algorithms, called matrix sparsification, approximates a matrix $A$ with a sparse matrix $A'$. Achlioptas and McSherry [2007] initiated a long line of work on spectral-norm sparsification, which aims to guarantee that $\|A'-A\|\leq \epsilon \|A\|$ for error parameter $\epsilon>0$. Various forms of matrix approximation motivate considering this problem with a guarantee according to the Schatten $p$-norm for general $p$, which includes the spectral norm as the special case $p=\infty$. We investigate the relation between fixed but different $p\neq q$, that is, whether sparsification in the Schatten $p$-norm implies (existentially and/or algorithmically) sparsification in the Schatten $q\text{-norm}$ with similar sparsity. An affirmative answer could be tremendously useful, as it will identify which value of $p$ to focus on. Our main finding is a surprising contrast between this question and the analogous case of $\ell_p$-norm sparsification for vectors: For vectors, the answer is affirmative for $p<q$ and negative for $p>q$, but for matrices we answer negatively for almost all sufficiently distinct $p\neq q$. In addition, our explicit constructions may be of independent interest.

In the envisioned beyond-fifth-generation (B5G) and sixth-generation (6G) scenarios which expect massive multiple-input multiple-output (mMIMO) and high frequency communications in the millimeter-wave (mmWave) and Terahertz (THz) bands, efficiency in both energy and spectrum is of increasing significance. To that extent, a novel ISAC framework called "sparse codesigned communication and radar (SCCR)" systems is described, which codesigns both communication and radar signals by a sparsification of the resource domain and the waveform spectrum domain. This improves the spectral and energy efficiency, but at the inherent cost of missing radar spectrum and irregular beampattern, and decreased throughput and diversity. Such challenges can however be corroborated, by leveraging various sparsity-robust signal processing techniques such as sparse radar reconstruction and index modulation (IM). In light of the above, the white paper aims to outlined the proposed article which provide an overview and a novel classification of the relevant state-of-the-art (SotA) methods and the implications of the challenges in the sparse codesign of the system, followed by a variety of novel SCCR frameworks.

2D-based Industrial Anomaly Detection has been widely discussed, however, multimodal industrial anomaly detection based on 3D point clouds and RGB images still has many untouched fields. Existing multimodal industrial anomaly detection methods directly concatenate the multimodal features, which leads to a strong disturbance between features and harms the detection performance. In this paper, we propose Multi-3D-Memory (M3DM), a novel multimodal anomaly detection method with hybrid fusion scheme: firstly, we design an unsupervised feature fusion with patch-wise contrastive learning to encourage the interaction of different modal features; secondly, we use a decision layer fusion with multiple memory banks to avoid loss of information and additional novelty classifiers to make the final decision. We further propose a point feature alignment operation to better align the point cloud and RGB features. Extensive experiments show that our multimodal industrial anomaly detection model outperforms the state-of-the-art (SOTA) methods on both detection and segmentation precision on MVTec-3D AD dataset. Code is available at //github.com/nomewang/M3DM.

We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Benefit from the quick development of deep learning techniques, salient object detection has achieved remarkable progresses recently. However, there still exists following two major challenges that hinder its application in embedded devices, low resolution output and heavy model weight. To this end, this paper presents an accurate yet compact deep network for efficient salient object detection. More specifically, given a coarse saliency prediction in the deepest layer, we first employ residual learning to learn side-output residual features for saliency refinement, which can be achieved with very limited convolutional parameters while keep accuracy. Secondly, we further propose reverse attention to guide such side-output residual learning in a top-down manner. By erasing the current predicted salient regions from side-output features, the network can eventually explore the missing object parts and details which results in high resolution and accuracy. Experiments on six benchmark datasets demonstrate that the proposed approach compares favorably against state-of-the-art methods, and with advantages in terms of simplicity, efficiency (45 FPS) and model size (81 MB).