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Previous work generally believes that improving the spatial invariance of convolutional networks is the key to object counting. However, after verifying several mainstream counting networks, we surprisingly found too strict pixel-level spatial invariance would cause overfit noise in the density map generation. In this paper, we try to use locally connected Gaussian kernels to replace the original convolution filter to estimate the spatial position in the density map. The purpose of this is to allow the feature extraction process to potentially stimulate the density map generation process to overcome the annotation noise. Inspired by previous work, we propose a low-rank approximation accompanied with translation invariance to favorably implement the approximation of massive Gaussian convolution. Our work points a new direction for follow-up research, which should investigate how to properly relax the overly strict pixel-level spatial invariance for object counting. We evaluate our methods on 4 mainstream object counting networks (i.e., MCNN, CSRNet, SANet, and ResNet-50). Extensive experiments were conducted on 7 popular benchmarks for 3 applications (i.e., crowd, vehicle, and plant counting). Experimental results show that our methods significantly outperform other state-of-the-art methods and achieve promising learning of the spatial position of objects.

This paper presents a new methodology that combines a multiple criteria sorting or ranking method with a project portfolio selection procedure. The multicriteria method permits to compare projects in terms of their priority assessed on the basis of a set of both qualitative and quantitative criteria. Then, a feasible set of projects, i.e. a portfolio, is selected according to the priority defined by the multiple criteria method. In addition, the portfolio must satisfy a set of resources constraints, e.g. budget available, as well as some logical constraints, e.g. related to projects to be selected together or projects mutually exclusive. The proposed portfolio selection methodology can be applied in different contexts. We present an application in the urban planning domain where our approach allows to select a set of urban projects on the basis of their priority, budgetary constraints and urban policy requirements. Given the increasing interest of historical cities to reuse their cultural heritage, we applied and tested our methodology in this context. In particular, we show how the methodology can support the prioritization of the interventions on buildings with some historical value in the historic city center of Naples (Italy), taking into account several points of view.

We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a distribution for the missing entries and present a robust framework, which minimizes the worst case error caused by the uncertainty about the missing data. We show that the proposed formulation, which naturally takes into account the dependency between different variables, ultimately reduces to a convex program, for which a customized and scalable solver can be delivered. In addition to a detailed analysis to deliver such solver, we also asymptoticly analyze the behavior of the proposed framework, and present technical discussions to estimate the required input parameters. We complement our analysis with experiments performed on synthetic, semi-synthetic, and real data, and show how the proposed formulation improves the prediction accuracy and robustness, and outperforms the competing techniques.

Understanding foggy image sequence in the driving scenes is critical for autonomous driving, but it remains a challenging task due to the difficulty in collecting and annotating real-world images of adverse weather. Recently, the self-training strategy has been considered a powerful solution for unsupervised domain adaptation, which iteratively adapts the model from the source domain to the target domain by generating target pseudo labels and re-training the model. However, the selection of confident pseudo labels inevitably suffers from the conflict between sparsity and accuracy, both of which will lead to suboptimal models. To tackle this problem, we exploit the characteristics of the foggy image sequence of driving scenes to densify the confident pseudo labels. Specifically, based on the two discoveries of local spatial similarity and adjacent temporal correspondence of the sequential image data, we propose a novel Target-Domain driven pseudo label Diffusion (TDo-Dif) scheme. It employs superpixels and optical flows to identify the spatial similarity and temporal correspondence, respectively and then diffuses the confident but sparse pseudo labels within a superpixel or a temporal corresponding pair linked by the flow. Moreover, to ensure the feature similarity of the diffused pixels, we introduce local spatial similarity loss and temporal contrastive loss in the model re-training stage. Experimental results show that our TDo-Dif scheme helps the adaptive model achieve 51.92% and 53.84% mean intersection-over-union (mIoU) on two publicly available natural foggy datasets (Foggy Zurich and Foggy Driving), which exceeds the state-of-the-art unsupervised domain adaptive semantic segmentation methods. Models and data can be found at //github.com/velor2012/TDo-Dif.

Wireless sensor networks are among the most promising technologies of the current era because of their small size, lower cost, and ease of deployment. With the increasing number of wireless sensors, the probability of generating missing data also rises. This incomplete data could lead to disastrous consequences if used for decision-making. There is rich literature dealing with this problem. However, most approaches show performance degradation when a sizable amount of data is lost. Inspired by the emerging field of graph signal processing, this paper performs a new study of a Sobolev reconstruction algorithm in wireless sensor networks. Experimental comparisons on several publicly available datasets demonstrate that the algorithm surpasses multiple state-of-the-art techniques by a maximum margin of 54%. We further show that this algorithm consistently retrieves the missing data even during massive data loss situations.

This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion problem has attracted much attention in the past decade, there is still lack of theoretical understanding when the observations are contaminated by heavy-tailed noises. Prior theory falls short of explaining the empirical results and is unable to capture the optimal dependence of the estimation error on the noise level. In this paper, we adopt an adaptive Huber loss to accommodate heavy-tailed noise, which is robust against large and possibly asymmetric errors when the parameter in the loss function is carefully designed to balance the Huberization biases and robustness to outliers. Then, we propose an efficient nonconvex algorithm via a balanced low-rank Burer-Monteiro matrix factorization and gradient decent with robust spectral initialization. We prove that under merely bounded second moment condition on the error distributions, rather than the sub-Gaussian assumption, the Euclidean error of the iterates generated by the proposed algorithm decrease geometrically fast until achieving a minimax-optimal statistical estimation error, which has the same order as that in the sub-Gaussian case. The key technique behind this significant advancement is a powerful leave-one-out analysis framework. The theoretical results are corroborated by our simulation studies.

In this paper, we work uniform error bounds for proper orthogonal decomposition reduced order modeling (POD-ROM) of Burgers equation, considering difference quotients (DQs), introduced in [23]. In particular, we study the optimality behavior of the DQ ROM error bounds by considering $L^2(\Omega)$ and $H^1_0(\Omega)$ POD spaces. We present some meaningful numerical tests checking the optimality error behavior. Based on our numerical observations, noDQ POD-ROM errors have an optimal behavior, while DQ POD-ROM errors demonstrate an optimality/super-optimality behavior. It is conjectured that this possibly occurs because the DQ inner products allow the time dependency in the ROM spaces to take into account.

We revisit the classic regular expression matching problem, that is, given a regular expression $R$ and a string $Q$, decide if $Q$ matches any of the strings specified by $R$. A standard textbook solution [Thompson, CACM 1968] solves this problem in $O(nm)$ time, where $n$ is the length of $Q$ and $m$ is the number of characters in $R$. More recently, several results that improve this bound by polylogarithmic factor have appeared. All of these solutions are essentially based on constructing and simulation a non-deterministic finite automaton. On the other hand, assuming the strong exponential time hypotheses we cannot solve regular expression $O((nm)^{1-\epsilon})$ [Backurs and Indyk, FOCS 2016]. Hence, a natural question is if we can design algorithms that can take advantage of other parameters of the problem to obtain more fine-grained bounds. We present the first algorithm for regular expression matching that can take advantage of sparsity of the automaton simulation. More precisely, we define the \emph{density}, $\Delta$, of the instance to be the total number of states in a simulation of a natural automaton for $R$. The density is always at most $nm+1$ but may be significantly smaller for many typical scenarios, e.g., when a string only matches a small part of the regular expression. Our main result is a new algorithm that solves the problem in $$O\left(\Delta \log \log \frac{nm}{\Delta} + n + m\right)$$ time. This result essentially replaces $nm$ with $\Delta$ in the complexity of regular expression matching. Prior to this work no non-trivial bound in terms of $\Delta$ was known. The key technical contribution is a new linear space representation of the classic position automaton that supports fast state-set transition computation in near-linear time in the size of the input and output state sets.

Depth maps are used in a wide range of applications from 3D rendering to 2D image effects such as Bokeh. However, those predicted by single image depth estimation (SIDE) models often fail to capture isolated holes in objects and/or have inaccurate boundary regions. Meanwhile, high-quality masks are much easier to obtain, using commercial auto-masking tools or off-the-shelf methods of segmentation and matting or even by manual editing. Hence, in this paper, we formulate a novel problem of mask-guided depth refinement that utilizes a generic mask to refine the depth prediction of SIDE models. Our framework performs layered refinement and inpainting/outpainting, decomposing the depth map into two separate layers signified by the mask and the inverse mask. As datasets with both depth and mask annotations are scarce, we propose a self-supervised learning scheme that uses arbitrary masks and RGB-D datasets. We empirically show that our method is robust to different types of masks and initial depth predictions, accurately refining depth values in inner and outer mask boundary regions. We further analyze our model with an ablation study and demonstrate results on real applications. More information can be found at //sooyekim.github.io/MaskDepth/ .

The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, if not better than, the original dense networks. Sparsity can reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.