A number of approaches have dealt with statistical assessment of self-similarity, and many of those are based on multiscale concepts. Most rely on certain distributional assumptions which are usually violated by real data traces, often characterized by large temporal or spatial mean level shifts, missing values or extreme observations. A novel, robust approach based on Theil-type weighted regression is proposed for estimating self-similarity in two-dimensional data (images). The method is compared to two traditional estimation techniques that use wavelet decompositions; ordinary least squares (OLS) and Abry-Veitch bias correcting estimator (AV). As an application, the suitability of the self-similarity estimate resulting from the the robust approach is illustrated as a predictive feature in the classification of digitized mammogram images as cancerous or non-cancerous. The diagnostic employed here is based on the properties of image backgrounds, which is typically an unused modality in breast cancer screening. Classification results show nearly 68% accuracy, varying slightly with the choice of wavelet basis, and the range of multiresolution levels used.
相關內容
The superposition of data sets with internal parametric self-similarity is a longstanding and widespread technique for the analysis of many types of experimental data across the physical sciences. Typically, this superposition is performed manually, or recently by one of a few automated algorithms. However, these methods are often heuristic in nature, are prone to user bias via manual data shifting or parameterization, and lack a native framework for handling uncertainty in both the data and the resulting model of the superposed data. In this work, we develop a data-driven, non-parametric method for superposing experimental data with arbitrary coordinate transformations, which employs Gaussian process regression to learn statistical models that describe the data, and then uses maximum a posteriori estimation to optimally superpose the data sets. This statistical framework is robust to experimental noise, and automatically produces uncertainty estimates for the learned coordinate transformations. Moreover, it is distinguished from black-box machine learning in its interpretability -- specifically, it produces a model that may itself be interrogated to gain insight into the system under study. We demonstrate these salient features of our method through its application to four representative data sets characterizing the mechanics of soft materials. In every case, our method replicates results obtained using other approaches, but with reduced bias and the addition of uncertainty estimates. This method enables a standardized, statistical treatment of self-similar data across many fields, producing interpretable data-driven models that may inform applications such as materials classification, design, and discovery.
Most methods for automated full-bore rock core image analysis (description, colour, properties distribution, etc.) are based on separate core column analyses. The core is usually imaged in a box because of the significant amount of time taken to get an image for each core column. The work presents an innovative method and algorithm for core columns extraction from core boxes. The conditions for core boxes imaging may differ tremendously. Such differences are disastrous for machine learning algorithms which need a large dataset describing all possible data variations. Still, such images have some standard features - a box and core. Thus, we can emulate different environments with a unique augmentation described in this work. It is called template-like augmentation (TLA). The method is described and tested on various environments, and results are compared on an algorithm trained on both 'traditional' data and a mix of traditional and TLA data. The algorithm trained with TLA data provides better metrics and can detect core on most new images, unlike the algorithm trained on data without TLA. The algorithm for core column extraction implemented in an automated core description system speeds up the core box processing by a factor of 20.
The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have nowadays gained particular attention. In this paper, we study two variants of this kind, namely, the Stochastic Variance Reduced Gradient Langevin Dynamics and the Stochastic Recursive Gradient Langevin Dynamics. We prove their convergence to the objective distribution in terms of KL-divergence under the sole assumptions of smoothness and Log-Sobolev inequality which are weaker conditions than those used in prior works for these algorithms. With the batch size and the inner loop length set to $\sqrt{n}$, the gradient complexity to achieve an $\epsilon$-precision is $\tilde{O}((n+dn^{1/2}\epsilon^{-1})\gamma^2 L^2\alpha^{-2})$, which is an improvement from any previous analyses. We also show some essential applications of our result to non-convex optimization.
Multi-camera vehicle tracking is one of the most complicated tasks in Computer Vision as it involves distinct tasks including Vehicle Detection, Tracking, and Re-identification. Despite the challenges, multi-camera vehicle tracking has immense potential in transportation applications including speed, volume, origin-destination (O-D), and routing data generation. Several recent works have addressed the multi-camera tracking problem. However, most of the effort has gone towards improving accuracy on high-quality benchmark datasets while disregarding lower camera resolutions, compression artifacts and the overwhelming amount of computational power and time needed to carry out this task on its edge and thus making it prohibitive for large-scale and real-time deployment. Therefore, in this work we shed light on practical issues that should be addressed for the design of a multi-camera tracking system to provide actionable and timely insights. Moreover, we propose a real-time city-scale multi-camera vehicle tracking system that compares favorably to computationally intensive alternatives and handles real-world, low-resolution CCTV instead of idealized and curated video streams. To show its effectiveness, in addition to integration into the Regional Integrated Transportation Information System (RITIS), we participated in the 2021 NVIDIA AI City multi-camera tracking challenge and our method is ranked among the top five performers on the public leaderboard.
For a given nonnegative matrix $A=(A_{ij})$, the matrix scaling problem asks whether $A$ can be scaled to a doubly stochastic matrix $XAY$ for some positive diagonal matrices $X,Y$. The Sinkhorn algorithm is a simple iterative algorithm, which repeats row-normalization $A_{ij} \leftarrow A_{ij}/\sum_{j}A_{ij}$ and column-normalization $A_{ij} \leftarrow A_{ij}/\sum_{i}A_{ij}$ alternatively. By this algorithm, $A$ converges to a doubly stochastic matrix in limit if and only if the bipartite graph associated with $A$ has a perfect matching. This property can decide the existence of a perfect matching in a given bipartite graph $G$, which is identified with the $0,1$-matrix $A_G$. Linial, Samorodnitsky, and Wigderson showed that a polynomial number of the Sinkhorn iterations for $A_G$ decides whether $G$ has a perfect matching. In this paper, we show an extension of this result: If $G$ has no perfect matching, then a polynomial number of the Sinkhorn iterations identifies a Hall blocker -- a certificate of the nonexistence of a perfect matching. Our analysis is based on an interpretation of the Sinkhorn algorithm as alternating KL-divergence minimization (Csisz\'{a}r and Tusn\'{a}dy 1984, Gietl and Reffel 2013) and its limiting behavior for a nonscalable matrix (Aas 2014). We also relate the Sinkhorn limit with parametric network flow, principal partition of polymatroids, and the Dulmage-Mendelsohn decomposition of a bipartite graph.
Recent advances in diffusion models bring the state-of-the art performance on image generation tasks. However, empirical results on previous research in diffusion models imply that there is an inverse correlation on performances for density estimation and sample generation. This paper analyzes that the inverse correlation arises because density estimation is mostly contributed from small diffusion time, whereas sample generation mainly depends on large diffusion time. However, training score network on both small and large diffusion time is demanding because of the loss imbalance issue. To successfully train the score network on both small and large diffusion time, this paper introduces a training technique, Soft Truncation, that softens the truncation time for every mini-batch update, which is universally applicable to any types of diffusion models. It turns out that Soft Truncation is equivalent to a diffusion model with a general weight, and we prove the variational bound of the general weighted diffusion model. In view of this variational bound, Soft Truncation becomes a natural way to train the score network. In experiments, Soft Truncation achieves the state-of-the-art performance on CIFAR-10, CelebA, CelebA-HQ $256\times 256$, and STL-10 datasets.
In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.
Multi-object tracking (MOT) is a crucial component of situational awareness in military defense applications. With the growing use of unmanned aerial systems (UASs), MOT methods for aerial surveillance is in high demand. Application of MOT in UAS presents specific challenges such as moving sensor, changing zoom levels, dynamic background, illumination changes, obscurations and small objects. In this work, we present a robust object tracking architecture aimed to accommodate for the noise in real-time situations. We propose a kinematic prediction model, called Deep Extended Kalman Filter (DeepEKF), in which a sequence-to-sequence architecture is used to predict entity trajectories in latent space. DeepEKF utilizes a learned image embedding along with an attention mechanism trained to weight the importance of areas in an image to predict future states. For the visual scoring, we experiment with different similarity measures to calculate distance based on entity appearances, including a convolutional neural network (CNN) encoder, pre-trained using Siamese networks. In initial evaluation experiments, we show that our method, combining scoring structure of the kinematic and visual models within a MHT framework, has improved performance especially in edge cases where entity motion is unpredictable, or the data presents frames with significant gaps.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
A key requirement for the success of supervised deep learning is a large labeled dataset - a condition that is difficult to meet in medical image analysis. Self-supervised learning (SSL) can help in this regard by providing a strategy to pre-train a neural network with unlabeled data, followed by fine-tuning for a downstream task with limited annotations. Contrastive learning, a particular variant of SSL, is a powerful technique for learning image-level representations. In this work, we propose strategies for extending the contrastive learning framework for segmentation of volumetric medical images in the semi-supervised setting with limited annotations, by leveraging domain-specific and problem-specific cues. Specifically, we propose (1) novel contrasting strategies that leverage structural similarity across volumetric medical images (domain-specific cue) and (2) a local version of the contrastive loss to learn distinctive representations of local regions that are useful for per-pixel segmentation (problem-specific cue). We carry out an extensive evaluation on three Magnetic Resonance Imaging (MRI) datasets. In the limited annotation setting, the proposed method yields substantial improvements compared to other self-supervision and semi-supervised learning techniques. When combined with a simple data augmentation technique, the proposed method reaches within 8% of benchmark performance using only two labeled MRI volumes for training, corresponding to only 4% (for ACDC) of the training data used to train the benchmark.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191