This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of rank-structured functions that can be seen as deep neural networks with a sparse architecture related to the tree and multilinear activation functions. For learning in a given model class, we exploit the fact that tree-based tensor formats are multilinear models and recast the problem of risk minimization over a nonlinear set into a succession of learning problems with linear models. Suitable changes of representation yield numerically stable learning problems and allow to exploit sparsity. For high-dimensional problems or when only a small data set is available, the selection of a good model class is a critical issue. For a given tree, the selection of the tuple of tree-based ranks that minimize the risk is a combinatorial problem. Here, we propose a rank adaptation strategy which provides in practice a good convergence of the risk as a function of the model class complexity. Finding a good tree is also a combinatorial problem, which can be related to the choice of a particular sparse architecture for deep neural networks. Here, we propose a stochastic algorithm for minimizing the complexity of the representation of a given function over a class of trees with a given arity, allowing changes in the topology of the tree. This tree optimization algorithm is then included in a learning scheme that successively adapts the tree and the corresponding tree-based ranks. Contrary to classical learning algorithms for nonlinear model classes, the proposed algorithms are numerically stable, reliable, and require only a low level expertise of the user.
In this paper, we confront the problem of deep learning's big labeled data requirements, offer a rule based strategy for extreme augmentation of small data sets and apply that strategy with the image to image translation model by Isola et al. (2016) to automate cel style cartoon coloring with very limited training data. While our experimental results using geometric rules and transformations demonstrate the performance of our methods on an image translation task with industry applications in art, design and animation, we also propose the use of rules on partial data sets as a generalizable small data strategy, potentially applicable across data types and domains.
Deep neural networks suffer from over-fitting and catastrophic forgetting when trained with small data. One natural remedy for this problem is data augmentation, which has been recently shown to be effective. However, previous works either assume that intra-class variances can always be generalized to new classes, or employ naive generation methods to hallucinate finite examples without modeling their latent distributions. In this work, we propose Covariance-Preserving Adversarial Augmentation Networks to overcome existing limits of low-shot learning. Specifically, a novel Generative Adversarial Network is designed to model the latent distribution of each novel class given its related base counterparts. Since direct estimation of novel classes can be inductively biased, we explicitly preserve covariance information as the `variability' of base examples during the generation process. Empirical results show that our model can generate realistic yet diverse examples, leading to substantial improvements on the ImageNet benchmark over the state of the art.
Automatic brain tumor segmentation plays an important role for diagnosis, surgical planning and treatment assessment of brain tumors. Deep convolutional neural networks (CNNs) have been widely used for this task. Due to the relatively small data set for training, data augmentation at training time has been commonly used for better performance of CNNs. Recent works also demonstrated the usefulness of using augmentation at test time, in addition to training time, for achieving more robust predictions. We investigate how test-time augmentation can improve CNNs' performance for brain tumor segmentation. We used different underpinning network structures and augmented the image by 3D rotation, flipping, scaling and adding random noise at both training and test time. Experiments with BraTS 2018 training and validation set show that test-time augmentation helps to improve the brain tumor segmentation accuracy and obtain uncertainty estimation of the segmentation results.
Learning to follow human instructions is a long-pursued goal in artificial intelligence. The task becomes particularly challenging if no prior knowledge of the employed language is assumed while relying only on a handful of examples to learn from. Work in the past has relied on hand-coded components or manually engineered features to provide strong inductive biases that make learning in such situations possible. In contrast, here we seek to establish whether this knowledge can be acquired automatically by a neural network system through a two phase training procedure: A (slow) offline learning stage where the network learns about the general structure of the task and a (fast) online adaptation phase where the network learns the language of a new given speaker. Controlled experiments show that when the network is exposed to familiar instructions but containing novel words, the model adapts very efficiently to the new vocabulary. Moreover, even for human speakers whose language usage can depart significantly from our artificial training language, our network can still make use of its automatically acquired inductive bias to learn to follow instructions more effectively.
As a promising area in artificial intelligence, a new learning paradigm, called Small Sample Learning (SSL), has been attracting prominent research attention in the recent years. In this paper, we aim to present a survey to comprehensively introduce the current techniques proposed on this topic. Specifically, current SSL techniques can be mainly divided into two categories. The first category of SSL approaches can be called "concept learning", which emphasizes learning new concepts from only few related observations. The purpose is mainly to simulate human learning behaviors like recognition, generation, imagination, synthesis and analysis. The second category is called "experience learning", which usually co-exists with the large sample learning manner of conventional machine learning. This category mainly focuses on learning with insufficient samples, and can also be called small data learning in some literatures. More extensive surveys on both categories of SSL techniques are introduced and some neuroscience evidences are provided to clarify the rationality of the entire SSL regime, and the relationship with human learning process. Some discussions on the main challenges and possible future research directions along this line are also presented.
Deep learning approaches have been rapidly adopted across a wide range of fields because of their accuracy and flexibility, but require large labeled training datasets. This presents a fundamental problem for applications with limited, expensive, or private data (i.e. small data), such as human pose and behavior estimation/tracking which could be highly personalized. In this paper, we present a semi-supervised data augmentation approach that can synthesize large scale labeled training datasets using 3D graphical engines based on a physically-valid low dimensional pose descriptor. To evaluate the performance of our synthesized datasets in training deep learning-based models, we generated a large synthetic human pose dataset, called ScanAva using 3D scans of only 7 individuals based on our proposed augmentation approach. A state-of-the-art human pose estimation deep learning model then was trained from scratch using our ScanAva dataset and could achieve the pose estimation accuracy of 91.2% at PCK0.5 criteria after applying an efficient domain adaptation on the synthetic images, in which its pose estimation accuracy was comparable to the same model trained on large scale pose data from real humans such as MPII dataset and much higher than the model trained on other synthetic human dataset such as SURREAL.
Learning from small amounts of labeled data is a challenge in the area of deep learning. This is currently addressed by Transfer Learning where one learns the small data set as a transfer task from a larger source dataset. Transfer Learning can deliver higher accuracy if the hyperparameters and source dataset are chosen well. One of the important parameters is the learning rate for the layers of the neural network. We show through experiments on the ImageNet22k and Oxford Flowers datasets that improvements in accuracy in range of 127% can be obtained by proper choice of learning rates. We also show that the images/label parameter for a dataset can potentially be used to determine optimal learning rates for the layers to get the best overall accuracy. We additionally validate this method on a sample of real-world image classification tasks from a public visual recognition API.
Recently proposed techniques for semi-supervised learning such as Temporal Ensembling and Mean Teacher have achieved state-of-the-art results in many important classification benchmarks. In this work, we expand the Mean Teacher approach to segmentation tasks and show that it can bring important improvements in a realistic small data regime using a publicly available multi-center dataset from the Magnetic Resonance Imaging (MRI) domain. We also devise a method to solve the problems that arise when using traditional data augmentation strategies for segmentation tasks on our new training scheme.
This article provides the role of big idea statisticians in future of Big Data Science. We describe the `United Statistical Algorithms' framework for comprehensive unification of traditional and novel statistical methods for modeling Small Data and Big Data, especially mixed data (discrete, continuous).
Bayesian model averaging (BMA) is the state of the art approach for overcoming model uncertainty. Yet, especially on small data sets, the results yielded by BMA might be sensitive to the prior over the models. Credal Model Averaging (CMA) addresses this problem by substituting the single prior over the models by a set of priors (credal set). Such approach solves the problem of how to choose the prior over the models and automates sensitivity analysis. We discuss various CMA algorithms for building an ensemble of logistic regressors characterized by different sets of covariates. We show how CMA can be appropriately tuned to the case in which one is prior-ignorant and to the case in which instead domain knowledge is available. CMA detects prior-dependent instances, namely instances in which a different class is more probable depending on the prior over the models. On such instances CMA suspends the judgment, returning multiple classes. We thoroughly compare different BMA and CMA variants on a real case study, predicting presence of Alpine marmot burrows in an Alpine valley. We find that BMA is almost a random guesser on the instances recognized as prior-dependent by CMA.
Machine learning methods are used today for most recognition problems. Convolutional Neural Networks (CNN) have time and again proved successful for many image processing tasks primarily for their architecture. In this paper we propose to apply CNN to small data sets like for example, personal albums or other similar environs where the size of training dataset is a limitation, within the framework of a proposed hybrid CNN-AIS model. We use Artificial Immune System Principles to enhance small size of training data set. A layer of Clonal Selection is added to the local filtering and max pooling of CNN Architecture. The proposed Architecture is evaluated using the standard MNIST dataset by limiting the data size and also with a small personal data sample belonging to two different classes. Experimental results show that the proposed hybrid CNN-AIS based recognition engine works well when the size of training data is limited in size
Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report, we analyze different methods for computing an important machine learing algorithm, namely Principal Component Analysis (PCA), and we comment on its limitations in supporting large datasets. The methods are analyzed and compared across two important metrics: time complexity and communication complexity. We consider the worst-case scenarios for both metrics, and we identify the software libraries that implement each method. The analysis in this report helps researchers and engineers in (i) understanding the main bottlenecks for scalability in different PCA algorithms, (ii) choosing the most appropriate method and software library for a given application and data set characteristics, and (iii) designing new scalable PCA algorithms.
Word embeddings -- distributed word representations that can be learned from unlabelled data -- have been shown to have high utility in many natural language processing applications. In this paper, we perform an extrinsic evaluation of five popular word embedding methods in the context of four sequence labelling tasks: POS-tagging, syntactic chunking, NER and MWE identification. A particular focus of the paper is analysing the effects of task-based updating of word representations. We show that when using word embeddings as features, as few as several hundred training instances are sufficient to achieve competitive results, and that word embeddings lead to improvements over OOV words and out of domain. Perhaps more surprisingly, our results indicate there is little difference between the different word embedding methods, and that simple Brown clusters are often competitive with word embeddings across all tasks we consider.
Most publicly available image quality databases have been created under highly controlled conditions by introducing graded simulated distortions onto high-quality photographs. However, images captured using typical real-world mobile camera devices are usually afflicted by complex mixtures of multiple distortions, which are not necessarily well-modeled by the synthetic distortions found in existing databases. The originators of existing legacy databases usually conducted human psychometric studies to obtain statistically meaningful sets of human opinion scores on images in a stringently controlled visual environment, resulting in small data collections relative to other kinds of image analysis databases. Towards overcoming these limitations, we designed and created a new database that we call the LIVE In the Wild Image Quality Challenge Database, which contains widely diverse authentic image distortions on a large number of images captured using a representative variety of modern mobile devices. We also designed and implemented a new online crowdsourcing system, which we have used to conduct a very large-scale, multi-month image quality assessment subjective study. Our database consists of over 350000 opinion scores on 1162 images evaluated by over 7000 unique human observers. Despite the lack of control over the experimental environments of the numerous study participants, we demonstrate excellent internal consistency of the subjective dataset. We also evaluate several top-performing blind Image Quality Assessment algorithms on it and present insights on how mixtures of distortions challenge both end users as well as automatic perceptual quality prediction models.
Multivariate classification methods using explanatory and predictive models are necessary for characterizing subgroups of patients according to their risk profiles. Popular methods include logistic regression and classification trees with performances that vary according to the nature and the characteristics of the dataset. In the context of imported malaria, we aimed at classifying severity criteria based on a heterogeneous patient population. We investigated these approaches by implementing two different strategies: L1 logistic regression (L1LR) that models a single global solution and classification trees that model multiple local solutions corresponding to discriminant subregions of the feature space. For each strategy, we built a standard model, and a sparser version of it. As an alternative to pruning, we explore a promising approach that first constrains the tree model with an L1LR-based feature selection, an approach we called L1LR-Tree. The objective is to decrease its vulnerability to small data variations by removing variables corresponding to unstable local phenomena. Our study is twofold: i) from a methodological perspective comparing the performances and the stability of the three previous methods, i.e L1LR, classification trees and L1LR-Tree, for the classification of severe forms of imported malaria, and ii) from an applied perspective improving the actual classification of severe forms of imported malaria by identifying more personalized profiles predictive of several clinical criteria based on variables dismissed for the clinical definition of the disease. The main methodological results show that the combined method L1LR-Tree builds sparse and stable models that significantly predicts the different severity criteria and outperforms all the other methods in terms of accuracy.
We derive a statistical model for estimation of a dendrogram from single linkage hierarchical clustering (SLHC) that takes account of uncertainty through noise or corruption in the measurements of separation of data. Our focus is on just the estimation of the hierarchy of partitions afforded by the dendrogram, rather than the heights in the latter. The concept of estimating this "dendrogram structure'' is introduced, and an approximate maximum likelihood estimator (MLE) for the dendrogram structure is described. These ideas are illustrated by a simple Monte Carlo simulation that, at least for small data sets, suggests the method outperforms SLHC in the presence of noise.
Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs overfit quickly. We present an efficient Bayesian CNN, offering better robustness to over-fitting on small data than traditional approaches. This is by placing a probability distribution over the CNN's kernels. We approximate our model's intractable posterior with Bernoulli variational distributions, requiring no additional model parameters. On the theoretical side, we cast dropout network training as approximate inference in Bayesian neural networks. This allows us to implement our model using existing tools in deep learning with no increase in time complexity, while highlighting a negative result in the field. We show a considerable improvement in classification accuracy compared to standard techniques and improve on published state-of-the-art results for CIFAR-10.
We study large-scale classification problems in changing environments where a small part of the dataset is modified, and the effect of the data modification must be quickly incorporated into the classifier. When the entire dataset is large, even if the amount of the data modification is fairly small, the computational cost of re-training the classifier would be prohibitively large. In this paper, we propose a novel method for efficiently incorporating such a data modification effect into the classifier without actually re-training it. The proposed method provides bounds on the unknown optimal classifier with the cost only proportional to the size of the data modification. We demonstrate through numerical experiments that the proposed method provides sufficiently tight bounds with negligible computational costs, especially when a small part of the dataset is modified in a large-scale classification problem.
Relatively small data sets available for expression recognition research make the training of deep networks for expression recognition very challenging. Although fine-tuning can partially alleviate the issue, the performance is still below acceptable levels as the deep features probably contain redun- dant information from the pre-trained domain. In this paper, we present FaceNet2ExpNet, a novel idea to train an expression recognition network based on static images. We first propose a new distribution function to model the high-level neurons of the expression network. Based on this, a two-stage training algorithm is carefully designed. In the pre-training stage, we train the convolutional layers of the expression net, regularized by the face net; In the refining stage, we append fully- connected layers to the pre-trained convolutional layers and train the whole network jointly. Visualization shows that the model trained with our method captures improved high-level expression semantics. Evaluations on four public expression databases, CK+, Oulu-CASIA, TFD, and SFEW demonstrate that our method achieves better results than state-of-the-art.