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This paper introduces a Video Quality Assessment (VQA) problem that has received little attention in the literature, called the latent resolution prediction problem. The problem arises when images or videos are upscaled from their native resolution and are reported as having a higher resolution than their native resolution. This paper formulates the problem, constructs a dataset for training and evaluation, and introduces several machine learning algorithms, including two Convolutional Neural Networks (CNNs), to address this problem. Experiments indicate that some proposed methods can predict the latent video resolution with about 95% accuracy., Comment: Submitted in ICIP conference

Shape modeling is a challenging task with many potential applications in computer vision and medical imaging. There are many shape modeling methods in the literature, each with its advantages and applications. However, many shape modeling methods have difficulties handling shapes that have missing pieces or outliers. In this regard, this paper introduces shape denoising, a fundamental problem in shape modeling that lies at the core of many computer vision and medical imaging applications and has not received enough attention in the literature. The paper introduces six types of noise that can be used to perturb shapes as well as an objective measure for the noise level and for comparing methods on their shape denoising capabilities. Finally, the paper evaluates seven methods capable of accomplishing this task, of which six are based on deep learning, including some generative models., Comment: 4 pages, 2 figures, International Conference on Image Processing (ICIP)

Big-data applications often involve a vast number of observations and features, creating new challenges for variable selection and parameter estimation. This paper presents a novel technique called ``slow kill,'' which utilizes nonconvex constrained optimization, adaptive $\ell_2$-shrinkage, and increasing learning rates. The fact that the problem size can decrease during the slow kill iterations makes it particularly effective for large-scale variable screening. The interaction between statistics and optimization provides valuable insights into controlling quantiles, stepsize, and shrinkage parameters in order to relax the regularity conditions required to achieve the desired level of statistical accuracy. Experimental results on real and synthetic data show that slow kill outperforms state-of-the-art algorithms in various situations while being computationally efficient for large-scale data.

Neural networks are usually trained with different variants of gradient descent based optimization algorithms such as stochastic gradient descent or the Adam optimizer. Recent theoretical work states that the critical points (where the gradient of the loss is zero) of two-layer ReLU networks with the square loss are not all local minima. However, in this work we will explore an algorithm for training two-layer neural networks with ReLU-like activation and the square loss that alternatively finds the critical points of the loss function analytically for one layer while keeping the other layer and the neuron activation pattern fixed. Experiments indicate that this simple algorithm can find deeper optima than Stochastic Gradient Descent or the Adam optimizer, obtaining significantly smaller training loss values on four out of the five real datasets evaluated. Moreover, the method is faster than the gradient descent methods and has virtually no tuning parameters., Comment: 17 pages, 11 figures

Stock market and cryptocurrency forecasting is very important to investors as they aspire to achieve even the slightest improvement to their buy or hold strategies so that they may increase profitability. However, obtaining accurate and reliable predictions is challenging, noting that accuracy does not equate to reliability, especially when financial time-series forecasting is applied owing to its complex and chaotic tendencies. To mitigate this complexity, this study provides a comprehensive method for forecasting financial time series based on tactical input output feature mapping techniques using machine learning (ML) models. During the prediction process, selecting the relevant indicators is vital to obtaining the desired results. In the financial field, limited attention has been paid to this problem with ML solutions. We investigate the use of feature selection with annealing (FSA) for the first time in this field, and we apply the least absolute shrinkage and selection operator (Lasso) method to select the features from more than 1,000 candidates obtained from 26 technical classifiers with different periods and lags. Boruta (BOR) feature selection, a wrapper method, is used as a baseline for comparison. Logistic regression (LR), extreme gradient boosting (XGBoost), and long short-term memory (LSTM) are then applied to the selected features for forecasting purposes using 10 different financial datasets containing cryptocurrencies and stocks. The dependent variables consisted of daily logarithmic returns and trends. The mean-squared error for regression, area under the receiver operating characteristic curve, and classification accuracy were used to evaluate model performance, and the statistical significance of the forecasting results was tested using paired t-tests. Experiments indicate that the FSA algorithm increased the performance of ML models, regardless of problem type., Comment: 37 pages, 1 figures and 12 tables

Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a provably robust clustering algorithm based on loss minimization that performs well on Gaussian mixture models with outliers. It provides theoretical guarantees that the algorithm obtains high accuracy with high probability under certain assumptions. Moreover, it can also be used as an initialization strategy for $k$-means clustering. Experiments on real-world large-scale datasets demonstrate the effectiveness of the algorithm when clustering a large number of clusters, and a $k$-means algorithm initialized by the algorithm outperforms many of the classic clustering methods in both speed and accuracy, while scaling well to large datasets such as ImageNet.

Screening feature selection methods are often used as a preprocessing step for reducing the number of variables before training step. Traditional screening methods only focus on dealing with complete high dimensional datasets. Modern datasets not only have higher dimension and larger sample size, but also have properties such as streaming input, sparsity and concept drift. Therefore a considerable number of online feature selection methods were introduced to handle these kind of problems in recent years. Online screening methods are one of the categories of online feature selection methods. The methods that we proposed in this research are capable of handling all three situations mentioned above. Our research study focuses on classification datasets. Our experiments show proposed methods can generate the same feature importance as their offline version with faster speed and less storage consumption. Furthermore, the results show that online screening methods with integrated model adaptation have a higher true feature detection rate than without model adaptation on data streams with the concept drift property. Among the two large real datasets that potentially have the concept drift property, online screening methods with model adaptation show advantages in either saving computing time and space, reducing model complexity, or improving prediction accuracy., Comment: 8 figures, 30 pages

Neural networks are popular and useful in many fields, but they have the problem of giving high confidence responses for examples that are away from the training data. This makes the neural networks very confident in their prediction while making gross mistakes, thus limiting their reliability for safety-critical applications such as autonomous driving, space exploration, etc. This paper introduces a novel neuron generalization that has the standard dot-product-based neuron and the {\color{black} radial basis function (RBF)} neuron as two extreme cases of a shape parameter. Using a rectified linear unit (ReLU) as the activation function results in a novel neuron that has compact support, which means its output is zero outside a bounded domain. To address the difficulties in training the proposed neural network, it introduces a novel training method that takes a pretrained standard neural network that is fine-tuned while gradually increasing the shape parameter to the desired value. The theoretical findings of the paper are a bound on the gradient of the proposed neuron and a proof that a neural network with such neurons has the universal approximation property. This means that the network can approximate any continuous and integrable function with an arbitrary degree of accuracy. The experimental findings on standard benchmark datasets show that the proposed approach has smaller test errors than state-of-the-art competing methods and outperforms the competing methods in detecting out-of-distribution samples on two out of three datasets., Comment: 13 pages, 6 figures

In many fields such as bioinformatics, high energy physics, power distribution, etc., it is desirable to learn non-linear models where a small number of variables are selected and the interaction between them is explicitly modeled to predict the response. In principle, neural networks (NNs) could accomplish this task since they can model non-linear feature interactions very well. However, NNs require large amounts of training data to have a good generalization. In this paper we study the datastarved regime where a NN is trained on a relatively small amount of training data. For that purpose we study feature selection for NNs, which is known to improve generalization for linear models. As an extreme case of data with feature selection and feature interactions we study the XOR-like data with irrelevant variables. We experimentally observed that the cross-entropy loss function on XOR-like data has many non-equivalent local optima, and the number of local optima grows exponentially with the number of irrelevant variables. To deal with the local minima and for feature selection we propose a node pruning and feature selection algorithm that improves the capability of NNs to find better local minima even when there are irrelevant variables. Finally, we show that the performance of a NN on real datasets can be improved using pruning, obtaining compact networks on a small number of features, with good prediction and interpretability.

Artificial Neural Networks form the basis of very powerful learning methods. It has been observed that a naive application of fully connected neural networks to data with many irrelevant variables often leads to overfitting. In an attempt to circumvent this issue, a prior knowledge pertaining to what features are relevant and their possible feature interactions can be encoded into these networks. In this work, we use decision trees to capture such relevant features and their interactions and define a mapping to encode extracted relationships into a neural network. This addresses the initialization related concern of fully connected neural networks. At the same time through feature selection it enables learning of compact representations compared to state of the art tree-based approaches. Empirical evaluations and simulation studies show the superiority of such an approach over fully connected neural networks and tree-based approaches

Artificial neural networks (ANNs) especially deep convolutional networks are very popular these days and have been proved to successfully offer quite reliable solutions to many vision problems. However, the use of deep neural networks is widely impeded by their intensive computational and memory cost. In this paper, we propose a novel efficient network pruning method that is suitable for both non-structured and structured channel-level pruning. Our proposed method tightens a sparsity constraint by gradually removing network parameters or filter channels based on a criterion and a schedule. The attractive fact that the network size keeps dropping throughout the iterations makes it suitable for the pruning of any untrained or pre-trained network. Because our method uses a $L_0$ constraint instead of the $L_1$ penalty, it does not introduce any bias in the training parameters or filter channels. Furthermore, the $L_0$ constraint makes it easy to directly specify the desired sparsity level during the network pruning process. Finally, experimental validation on extensive synthetic and real vision datasets show that the proposed method obtains better or competitive performance compared to other states of art network pruning methods.

Human beings are particularly good at reasoning and inference from just a few examples. When facing new tasks, humans will leverage knowledge and skills learned before, and quickly integrate them with the new task. In addition to learning by experimentation, human also learn socio-culturally through instructions and learning by example. In this way humans can learn much faster compared with most current artificial intelligence algorithms in many tasks. In this paper, we test the idea of speeding up machine learning through social learning. We argue that in solving real-world problems, especially when the task is designed by humans, and/or for humans, there are typically instructions from user manuals and/or human experts which give guidelines on how to better accomplish the tasks. We argue that these instructions have tremendous value in designing a reinforcement learning system which can learn in human fashion, and we test the idea by playing the Atari games Tennis and Pong. We experimentally demonstrate that the instructions provide key information about the task, which can be used to decompose the learning task into sub-systems and construct options for the temporally extended planning, and dramatically accelerate the learning process.

Pruning neural network parameters is often viewed as a means to compress models, but pruning has also been motivated by the desire to prevent overfitting. This motivation is particularly relevant given the perhaps surprising observation that a wide variety of pruning approaches increase test accuracy despite sometimes massive reductions in parameter counts. To better understand this phenomenon, we analyze the behavior of pruning over the course of training, finding that pruning's benefit to generalization increases with pruning's instability (defined as the drop in test accuracy immediately following pruning). We demonstrate that this "generalization-stability tradeoff" is present across a wide variety of pruning settings and propose a mechanism for its cause: pruning regularizes similarly to noise injection. Supporting this, we find less pruning stability leads to more model flatness and the benefits of pruning do not depend on permanent parameter removal. These results explain the compatibility of pruning-based generalization improvements and the high generalization recently observed in overparameterized networks., Comment: NeurIPS 2020 conference paper

Filter or screening methods are often used as a preprocessing step for reducing the number of variables used by a learning algorithm in obtaining a classification or regression model. While there are many such filter methods, there is a need for an objective evaluation of these methods. Such an evaluation is needed to compare them with each other and also to answer whether they are at all useful, or a learning algorithm could do a better job without them. For this purpose, many popular screening methods are partnered in this paper with three regression learners and five classification learners and evaluated on ten real datasets to obtain accuracy criteria such as R-square and area under the ROC curve (AUC). The obtained results are compared through curve plots and comparison tables in order to find out whether screening methods help improve the performance of learning algorithms and how they fare with each other. Our findings revealed that the screening methods were useful in improving the prediction of the best learner on two regression and two classification datasets out of the ten datasets evaluated., Comment: 29 pages, 4 figures, 21 tables

Artificial neural networks (ANNs) may not be worth their computational/memory costs when used in mobile phones or embedded devices. Parameter-pruning algorithms combat these costs, with some algorithms capable of removing over 90% of an ANN's weights without harming the ANN's performance. Removing weights from an ANN is a form of regularization, but existing pruning algorithms do not significantly improve generalization error. We show that pruning ANNs can improve generalization if pruning targets large weights instead of small weights. Applying our pruning algorithm to an ANN leads to a higher image classification accuracy on CIFAR-10 data than applying the popular regularizer dropout. The pruning couples this higher accuracy with an 85% reduction of the ANN's parameter count.

Gaussian Mixture Models are one of the most studied and mature models in unsupervised learning. However, outliers are often present in the data and could influence the cluster estimation. In this paper, we study a new model that assumes that data comes from a mixture of a number of Gaussians as well as a uniform ``background'' component assumed to contain outliers and other non-interesting observations. We develop a novel method based on robust loss minimization that performs well in clustering such GMM with a uniform background. We give theoretical guarantees for our clustering algorithm to obtain best clustering results with high probability. Besides, we show that the result of our algorithm does not depend on initialization or local optima, and the parameter tuning is an easy task. By numeric simulations, we demonstrate that our algorithm enjoys high accuracy and achieves the best clustering results given a large enough sample size. Finally, experimental comparisons with typical clustering methods on real datasets witness the potential of our algorithm in real applications., Comment: 36 pages, 16 figures and 4 tables

Current online learning methods suffer issues such as lower convergence rates and limited capability to select important features compared to their offline counterparts. In this paper, a novel framework for online learning based on running averages is proposed. Many popular offline regularized methods such as Lasso, Elastic Net, Minimax Concave Penalty (MCP), and Feature Selection with Annealing (FSA) have their online versions introduced in this framework. The equivalence between the proposed online methods and their offline counterparts is proved, and then novel theoretical true support recovery and convergence guarantees are provided for some of the methods in this framework. Numerical experiments indicate that the proposed methods enjoy high true support recovery accuracy and a faster convergence rate compared with conventional online and offline algorithms. Finally, applications to large datasets are presented, where again the proposed framework shows competitive results compared to popular online and offline algorithms., Comment: This version has been accepted by Journal of Nonparametric Statistics

We propose random hinge forests, a simple, efficient, and novel variant of decision forests. Importantly, random hinge forests can be readily incorporated as a general component within arbitrary computation graphs that are optimized end-to-end with stochastic gradient descent or variants thereof. We derive random hinge forest and ferns, focusing on their sparse and efficient nature, their min-max margin property, strategies to initialize them for arbitrary network architectures, and the class of optimizers most suitable for optimizing random hinge forest. The performance and versatility of random hinge forests are demonstrated by experiments incorporating a variety of of small and large UCI machine learning data sets and also ones involving the MNIST, Letter, and USPS image datasets. We compare random hinge forests with random forests and the more recent backpropagating deep neural decision forests.

Tree ensembles are flexible predictive models that can capture relevant variables and to some extent their interactions in a compact and interpretable manner. Most algorithms for obtaining tree ensembles are based on versions of boosting or Random Forest. Previous work showed that boosting algorithms exhibit a cyclic behavior of selecting the same tree again and again due to the way the loss is optimized. At the same time, Random Forest is not based on loss optimization and obtains a more complex and less interpretable model. In this paper we present a novel method for obtaining compact tree ensembles by growing a large pool of trees in parallel with many independent boosting threads and then selecting a small subset and updating their leaf weights by loss optimization. We allow for the trees in the initial pool to have different depths which further helps with generalization. Experiments on real datasets show that the obtained model has usually a smaller loss than boosting, which is also reflected in a lower misclassification error on the test set., Comment: Comparison with Random Forest included in the results section

When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the face of a 40 year old to be more similar to the face of a 30 year old than to a baby face. We introduce a novel manifold approximation method, parameterized principal component analysis (PPCA) that models data with linear subspaces that change continuously according to the extra parameter of contextual information (e.g. age), instead of ad-hoc atlases. Special care has been taken in the loss function and the optimization method to encourage smoothly changing subspaces across the parameter values. The approach ensures that each observation's projection will share information with observations that have similar parameter values, but not with observations that have large parameter differences. We tested PPCA on artificial data based on known, smooth functions of an added parameter, as well as on three real datasets with different types of parameters. We compared PPCA to PCA, sparse PCA and to independent principal component analysis (IPCA), which groups observations by their parameter values and projects each group using PCA with no sharing of information for different groups. PPCA recovers the known functions with less error and projects the datasets' test set observations with consistently less reconstruction error than IPCA does. In some cases where the manifold is truly nonlinear, PCA outperforms all the other manifold approximation methods compared., Comment: 36 pages, 15 figures

Image denoising algorithms are evaluated using images corrupted by artificial noise, which may lead to incorrect conclusions about their performances on real noise. In this paper we introduce a dataset of color images corrupted by natural noise due to low-light conditions, together with spatially and intensity-aligned low noise images of the same scenes. We also introduce a method for estimating the true noise level in our images, since even the low noise images contain small amounts of noise. We evaluate the accuracy of our noise estimation method on real and artificial noise, and investigate the Poisson-Gaussian noise model. Finally, we use our dataset to evaluate six denoising algorithms: Active Random Field, BM3D, Bilevel-MRF, Multi-Layer Perceptron, and two versions of NL-means. We show that while the Multi-Layer Perceptron, Bilevel-MRF, and NL-means with soft threshold outperform BM3D on gray images with synthetic noise, they lag behind on our dataset., Comment: 27 pages, 11 figures

This paper presents a part-based face detection approach where the spatial relationship between the face parts is represented by a hidden 3D model with six parameters. The computational complexity of the search in the six dimensional pose space is addressed by proposing meaningful 3D pose candidates by image-based regression from detected face keypoint locations. The 3D pose candidates are evaluated using a parameter sensitive classifier based on difference features relative to the 3D pose. A compatible subset of candidates is then obtained by non-maximal suppression. Experiments on two standard face detection datasets show that the proposed 3D model based approach obtains results comparable to or better than state of the art., Comment: 14 pages, 11 figures

Many computer vision and medical imaging problems are faced with learning from large-scale datasets, with millions of observations and features. In this paper we propose a novel efficient learning scheme that tightens a sparsity constraint by gradually removing variables based on a criterion and a schedule. The attractive fact that the problem size keeps dropping throughout the iterations makes it particularly suitable for big data learning. Our approach applies generically to the optimization of any differentiable loss function, and finds applications in regression, classification and ranking. The resultant algorithms build variable screening into estimation and are extremely simple to implement. We provide theoretical guarantees of convergence and selection consistency. In addition, one dimensional piecewise linear response functions are used to account for nonlinearity and a second order prior is imposed on these functions to avoid overfitting. Experiments on real and synthetic data show that the proposed method compares very well with other state of the art methods in regression, classification and ranking while being computationally very efficient and scalable., Comment: 18 pages, 9 figures

Dasgupta and Shulman showed that a two-round variant of the EM algorithm can learn mixture of Gaussian distributions with near optimal precision with high probability if the Gaussian distributions are well separated and if the dimension is sufficiently high. In this paper, we generalize their theory to learning mixture of high-dimensional Bernoulli templates. Each template is a binary vector, and a template generates examples by randomly switching its binary components independently with a certain probability. In computer vision applications, a binary vector is a feature map of an image, where each binary component indicates whether a local feature or structure is present or absent within a certain cell of the image domain. A Bernoulli template can be considered as a statistical model for images of objects (or parts of objects) from the same category. We show that the two-round EM algorithm can learn mixture of Bernoulli templates with near optimal precision with high probability, if the Bernoulli templates are sufficiently different and if the number of features is sufficiently high. We illustrate the theoretical results by synthetic and real examples., Comment: 27 pages, 8 figures

The Artificial Prediction Market is a recent machine learning technique for multi-class classification, inspired from the financial markets. It involves a number of trained market participants that bet on the possible outcomes and are rewarded if they predict correctly. This paper generalizes the scope of the Artificial Prediction Markets to regression, where there are uncountably many possible outcomes and the error is usually the MSE. For that, we introduce the reward kernel that rewards each participant based on its prediction error and we derive the price equations. Using two reward kernels we obtain two different learning rules, one of which is approximated using Hermite-Gauss quadrature. The market setting makes it easy to aggregate specialized regressors that only predict when an observation falls into their specialization domain. Experiments show that regression markets based on the two learning rules outperform Random Forest Regression on many UCI datasets and are rarely outperformed.

Object parsing and segmentation from point clouds are challenging tasks because the relevant data is available only as thin structures along object boundaries or other features, and is corrupted by large amounts of noise. To handle this kind of data, flexible shape models are desired that can accurately follow the object boundaries. Popular models such as Active Shape and Active Appearance models lack the necessary flexibility for this task, while recent approaches such as the Recursive Compositional Models make model simplifications in order to obtain computational guarantees. This paper investigates a hierarchical Bayesian model of shape and appearance in a generative setting. The input data is explained by an object parsing layer, which is a deformation of a hidden PCA shape model with Gaussian prior. The paper also introduces a novel efficient inference algorithm that uses informed data-driven proposals to initialize local searches for the hidden variables. Applied to the problem of object parsing from structured point clouds such as edge detection images, the proposed approach obtains state of the art parsing errors on two standard datasets without using any intensity information., Comment: 13 pages, 16 figures

Prediction markets are used in real life to predict outcomes of interest such as presidential elections. This paper presents a mathematical theory of artificial prediction markets for supervised learning of conditional probability estimators. The artificial prediction market is a novel method for fusing the prediction information of features or trained classifiers, where the fusion result is the contract price on the possible outcomes. The market can be trained online by updating the participants' budgets using training examples. Inspired by the real prediction markets, the equations that govern the market are derived from simple and reasonable assumptions. Efficient numerical algorithms are presented for solving these equations. The obtained artificial prediction market is shown to be a maximum likelihood estimator. It generalizes linear aggregation, existent in boosting and random forest, as well as logistic regression and some kernel methods. Furthermore, the market mechanism allows the aggregation of specialized classifiers that participate only on specific instances. Experimental comparisons show that the artificial prediction markets often outperform random forest and implicit online learning on synthetic data and real UCI datasets. Moreover, an extensive evaluation for pelvic and abdominal lymph node detection in CT data shows that the prediction market improves adaboost's detection rate from 79.6% to 81.2% at 3 false positives/volume., Comment: 29 pages, 8 figures

Dimension reduction and variable selection are performed routinely in case-control studies, but the literature on the theoretical aspects of the resulting estimates is scarce. We bring our contribution to this literature by studying estimators obtained via L1 penalized likelihood optimization. We show that the optimizers of the L1 penalized retrospective likelihood coincide with the optimizers of the L1 penalized prospective likelihood. This extends the results of Prentice and Pyke (1979), obtained for non-regularized likelihoods. We establish both the sup-norm consistency of the odds ratio, after model selection, and the consistency of subset selection of our estimators. The novelty of our theoretical results consists in the study of these properties under the case-control sampling scheme. Our results hold for selection performed over a large collection of candidate variables, with cardinality allowed to depend and be greater than the sample size. We complement our theoretical results with a novel approach of determining data driven tuning parameters, based on the bisection method. The resulting procedure offers significant computational savings when compared with grid search based methods. All our numerical experiments support strongly our theoretical findings., Comment: 32 pages, 5 figures, 3 tables

This paper studies sparse density estimation via $\ell_1$ penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities and that it yields minimax adaptive density estimates. These results are based on a general sparsity oracle inequality that the SPADES estimates satisfy. We offer a data driven method for the choice of the tuning parameter used in the construction of SPADES. The method uses the generalized bisection method first introduced in \citebb09. The suggested procedure bypasses the need for a grid search and offers substantial computational savings. We complement our theoretical results with a simulation study that employs this method for approximations of one and two-dimensional densities with mixtures. The numerical results strongly support our theoretical findings., Comment: Published in at http://dx.doi.org/10.1214/09-AOS790 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)