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Part-based representations have been shown to be very useful for image classification. Learning part-based models is often viewed as a two-stage problem. First, a collection of informative parts is discovered, using heuristics that promote…
We propose an algorithm for optimizing the parameters of single hidden layer neural networks. Specifically, we derive a blockwise difference-of-convex (DC) functions representation of the objective function. Based on the latter, we propose…
The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…
In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…
Pair-wise loss is an approach to metric learning that learns a semantic embedding by optimizing a loss function that encourages images from the same semantic class to be mapped closer than images from different classes. The literature…
Although traditional optimization methods focus on finding a single optimal solution, most objective functions in modern machine learning problems, especially those in deep learning, often have multiple or infinite numbers of optima.…
Automatic building extraction from aerial imagery has several applications in urban planning, disaster management, and change detection. In recent years, several works have adopted deep convolutional neural networks (CNNs) for building…
The problem of segmenting a given image into coherent regions is important in Computer Vision and many industrial applications require segmenting a known object into its components. Examples include identifying individual parts of a…
In this paper, we adopt a probability distribution estimation perspective to explore the optimization mechanisms of supervised classification using deep neural networks. We demonstrate that, when employing the Fenchel-Young loss, despite…
This paper proposes FREEtree, a tree-based method for high dimensional longitudinal data with correlated features. Popular machine learning approaches, like Random Forests, commonly used for variable selection do not perform well when there…
The choice of a loss function is an important factor when training neural networks for image restoration problems, such as single image super resolution. The loss function should encourage natural and perceptually pleasing results. A…
In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
We transpose an optimal control technique to the image segmentation problem. The idea is to consider image segmentation as a parameter estimation problem. The parameter to estimate is the color of the pixels of the image. We use the…
Besides serving as prediction models, classification trees are useful for finding important predictor variables and identifying interesting subgroups in the data. These functions can be compromised by weak split selection algorithms that…
Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable.…
We present multi-point optimization: an optimization technique that allows to train several models simultaneously without the need to keep the parameters of each one individually. The proposed method is used for a thorough empirical…
Hierarchical taxonomies are common in many contexts, and they are a very natural structure humans use to organise information. In machine learning, the family of methods that use the 'extra' information is called hierarchical…