We present an end-to-end learned algorithm for seeded segmentation. Our method is based on the Random Walker algorithm, where we predict the edge weights of the underlying graph using a convolutional neural network. This can be interpreted as learning context-dependent diffusivities for a linear diffusion process. Besides calculating the exact gradient for optimizing these diffusivities, we also propose simplifications that sparsely sample the gradient and still yield competitive results. The proposed method achieves the currently best results on a seeded version of the CREMI neuron segmentation challenge.
@cite_19 have pioneered the use of flexible nonparametric classifiers to determine the potentials in a Conditional GMRF. However, they opted for ensembles of decision trees and had to estimate the impact of each possible split on the loss function, making a number of approximations necessary.
@cite_19
2290283816 2126022166 2105693855 1982032418
This paper investigates the connections between two state of the art classifiers: decision forests (DFs, including decision jungles) and convolutional neural networks (CNNs). Decision forests are computationally efficient thanks to their conditional computation property (computation is confined to only a small region of the tree, the nodes along a single branch). CNNs achieve state of the art accuracy, thanks to their representation learning capabilities. We present a systematic analysis of how to fuse conditional computation with representation learning and achieve a continuum of hybrid models with different ratios of accuracy vs. efficiency. We call this new family of hybrid models conditional networks. Conditional networks can be thought of as: i) decision trees augmented with data transformation operators, or ii) CNNs, with block-diagonal sparse weight matrices, and explicit data routing functions. Experimental validation is performed on the common task of image classification on both the CIFAR and Imagenet datasets. Compared to state of the art CNNs, our hybrid models yield the same accuracy with a fraction of the compute cost and much smaller number of parameters. This paper studies two-class (or binary) classification of elements X in R k that allows for a reject option. Based on n independent copies of the pair of random variables (X,Y ) with X 2 R k and Y 2 0,1 , we consider classifiers f(X) that render three possible outputs: 0, 1 and R. The option R expresses doubt and is to be used for few observations that are hard to classify in an automatic way. Chow (1970) derived the optimal rule minimizing the risk P f(X) 6 Y, f(X) 6 R + dP f(X) = R . This risk function subsumes that the cost of making a wrong decision equals 1 and that of utilizing the reject option is d. We show that the classification problem hinges on the behavior of the regression function (x) = E(Y |X = x) near d and 1 d. (Here d 2 [0,1 2] as the other cases turn out to be trivial.) Classification rules can be categorized into plug-in estimators and empirical risk minimizers. Both types are considered here and we prove that the rates of convergence of the risk of any estimate depends on P | (X) d| + P | (X) (1 d)| and on the quality of the estimate for or an appropriate measure of the size of the class of classifiers, in case of plug-in rules and empirical risk minimizers, respectively. We extend the mathematical framework even further by dierentiating between costs associated with the two possible errors: predicting f(X) = 0 whilst Y = 1 and predicting f(X) = 1 whilst Y = 0. Such situations are common in, for instance, medical studies where misclassifying a sick patient as healthy is worse than the opposite. In this paper, a prototype wavelet-based neural-network classifier for recognizing power-quality disturbances is implemented and tested under various transient events. The discrete wavelet transform (DWT) technique is integrated with the probabilistic neural-network (PNN) model to construct the classifier. First, the multiresolution-analysis technique of DWT and the Parseval's theorem are employed to extract the energy distribution features of the distorted signal at different resolution levels. Then, the PNN classifies these extracted features to identify the disturbance type according to the transient duration and the energy features. Since the proposed methodology can reduce a great quantity of the distorted signal features without losing its original property, less memory space and computing time are required. Various transient events tested, such as momentary interruption, capacitor switching, voltage sag swell, harmonic distortion, and flicker show that the classifier can detect and classify different power disturbance types efficiently. Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0–1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general quantitative relationship between the risk as assessed using the 0–1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function—that it satisfies a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the...