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The estimation of nested functions (i.e., functions of functions) is one of the central reasons for the success and popularity of machine learning. Today, artificial neural networks are the predominant class of algorithms in this area, known as representational learning. Here, we introduce Representational Gradient Boosting (RGB), a nonparametric algorithm that estimates functions with multi-layer architectures obtained using backpropagation in the space of functions. RGB does not need to assume a functional form in the nodes or output (e.g., linear models or rectified linear units), but rather estimates these transformations. RGB can be seen as an optimized stacking procedure where a meta algorithm learns how to combine different classes of functions (e.g., Neural Networks (NN) and Gradient Boosting (GB)), while building and optimizing them jointly in an attempt to compensate each other’s weaknesses. This highlights a stark difference with current approaches to meta-learning that combine models only after they have been built independently. We showed that providing optimized stacking is one of the main advantages of RGB over current approaches. Additionally, due to the nested nature of RGB we also showed how it improves over GB in problems that have several high-order interactions. Finally, we investigate both theoretically and in practice the problem of recovering nested functions and the value of prior knowledge. [ABSTRACT FROM AUTHOR]

Using cross validation to select the best model from a library is standard practice in machine learning. Similarly, meta learning is a widely used technique where models previously developed are combined (mainly linearly) with the expectation of improving performance with respect to individual models. In this article we consider the Conditional Super Learner (CSL), an algorithm that selects the best model candidate from a library of models conditional on the covariates. The CSL expands the idea of using cross validation to select the best model and merges it with meta learning. We propose an optimization algorithm that finds a local minimum to the problem posed and proves that it converges at a rate faster than $O_p(n^{-1/4})$ O p (n - 1 / 4) . We offer empirical evidence that: (1) CSL is an excellent candidate to substitute stacking and (2) CLS is suitable for the analysis of Hierarchical problems. Additionally, implications for global interpretability are emphasized. [ABSTRACT FROM AUTHOR]

AutoML aims at best configuring learning systems automatically. It contains core subtasks of algorithm selection and hyper-parameter tuning. Previous approaches considered searching in the joint hyper-parameter space of all algorithms, which forms a huge but redundant space and causes an inefficient search. We tackle this issue in a cascaded algorithm selection way, which contains an upper-level process of algorithm selection and a lower-level process of hyper-parameter tuning for algorithms. While the lower-level process employs an anytime tuning approach, the upper-level process is naturally formulated as a multi-armed bandit, deciding which algorithm should be allocated one more piece of time for the lower-level tuning. To achieve the goal of finding the best configuration, we propose the Extreme-Region Upper Confidence Bound (ER-UCB) strategy. Unlike UCB bandits that maximize the mean of feedback distribution, ER-UCB maximizes the extreme-region of feedback distribution. We first consider stationary distributions and propose the ER-UCB-S algorithm that has $O(K\ln n)$ O (K ln n) regret upper bound with $K$ K arms and $n$ n trials. We then extend to non-stationary settings and propose the ER-UCB-N algorithm that has $O(Kn^\nu)$ O (K n ν) regret upper bound, where $\frac{2}{3}<\nu <1$ 2 3 < ν < 1 . Finally, empirical studies on synthetic and AutoML tasks verify the effectiveness of ER-UCB-S/N by their outperformance in corresponding settings. [ABSTRACT FROM AUTHOR]

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated as low-rank semi-definite programming (SDP) problems. Traditional formulations use the square loss, which is notorious for being sensitive to outliers. We propose to replace this with more robust noise models, including the $\ell _1$ ℓ 1 -loss and other nonconvex losses. However, the resultant optimization problem becomes difficult as the objective is no longer convex or smooth. To alleviate this problem, we design an efficient algorithm based on majorization-minimization. The crux is on constructing a good optimization surrogate, and we show that this surrogate can be efficiently obtained by the alternating direction method of multipliers (ADMM). By properly monitoring ADMM's convergence, the proposed algorithm is empirically efficient and also theoretically guaranteed to converge to a critical point. Extensive experiments are performed on four machine learning applications using both synthetic and real-world data sets. Results show that the proposed algorithm is not only fast but also has better performance than the state-of-the-arts. [ABSTRACT FROM AUTHOR]

The foundational assumption of machine learning is that the data under consideration is separable into classes; while intuitively reasonable, separability constraints have proven remarkably difficult to formulate mathematically. We believe this problem is rooted in the mismatch between existing statistical techniques and commonly encountered data; object representations are typically high dimensional but statistical techniques tend to treat high dimensions a degenerate case. To address this problem, we develop a dedicated statistical framework for machine learning in high dimensions. The framework derives from the observation that object relations form a natural hierarchy; this leads us to model objects as instances of a high dimensional, hierarchal generative processes. Using a distance based statistical technique, also developed in this paper, we show that in such generative processes, instances of each process in the hierarchy, are almost-always encapsulated by a distinctive-shell that excludes almost-all other instances. The result is shell theory, a statistical machine learning framework in which separability constraints (distinctive-shells) are formally derived from the assumed generative process. [ABSTRACT FROM AUTHOR]

The field of meta-learning, or learning-to-learn, has seen a dramatic rise in interest in recent years. Contrary to conventional approaches to AI where tasks are solved from scratch using a fixed learning algorithm, meta-learning aims to improve the learning algorithm itself, given the experience of multiple learning episodes. This paradigm provides an opportunity to tackle many conventional challenges of deep learning, including data and computation bottlenecks, as well as generalization. This survey describes the contemporary meta-learning landscape. We first discuss definitions of meta-learning and position it with respect to related fields, such as transfer learning and hyperparameter optimization. We then propose a new taxonomy that provides a more comprehensive breakdown of the space of meta-learning methods today. We survey promising applications and successes of meta-learning such as few-shot learning and reinforcement learning. Finally, we discuss outstanding challenges and promising areas for future research. [ABSTRACT FROM AUTHOR]

Stereo matching is one of the most popular techniques to estimate dense depth maps by finding the disparity between matching pixels on two, synchronized and rectified images. Alongside with the development of more accurate algorithms, the research community focused on finding good strategies to estimate the reliability, i.e., the confidence, of estimated disparity maps. This information proves to be a powerful cue to naively find wrong matches as well as to improve the overall effectiveness of a variety of stereo algorithms according to different strategies. In this paper, we review more than ten years of developments in the field of confidence estimation for stereo matching. We extensively discuss and evaluate existing confidence measures and their variants, from hand-crafted ones to the most recent, state-of-the-art learning based methods. We study the different behaviors of each measure when applied to a pool of different stereo algorithms and, for the first time in literature, when paired with a state-of-the-art deep stereo network. Our experiments, carried out on five different standard datasets, provide a comprehensive overview of the field, highlighting in particular both strengths and limitations of learning-based strategies. [ABSTRACT FROM AUTHOR]

While most existing multilabel ranking methods assume the availability of a single objective label ranking for each instance in the training set, this paper deals with a more common case where only subjective inconsistent rankings from multiple rankers are associated with each instance. Two ranking methods are proposed from the perspective of instances and rankers, respectively. The first method, Instance-oriented Preference Distribution Learning (IPDL), is to learn a latent preference distribution for each instance. IPDL generates a common preference distribution that is most compatible to all the personal rankings, and then learns a mapping from the instances to the preference distributions. The second method, Ranker-oriented Preference Distribution Learning (RPDL), is proposed by leveraging interpersonal inconsistency among rankers, to learn a unified model from personal preference distribution models of all rankers. These two methods are applied to natural scene images dataset and 3D facial expression dataset BU_3DFE. Experimental results show that IPDL and RPDL can effectively incorporate the information given by the inconsistent rankers, and perform remarkably better than the compared state-of-the-art multilabel ranking algorithms. [ABSTRACT FROM AUTHOR]

Curriculum learning (CL) is a training strategy that trains a machine learning model from easier data to harder data, which imitates the meaningful learning order in human curricula. As an easy-to-use plug-in, the CL strategy has demonstrated its power in improving the generalization capacity and convergence rate of various models in a wide range of scenarios such as computer vision and natural language processing etc. In this survey article, we comprehensively review CL from various aspects including motivations, definitions, theories, and applications. We discuss works on curriculum learning within a general CL framework, elaborating on how to design a manually predefined curriculum or an automatic curriculum. In particular, we summarize existing CL designs based on the general framework of Difficulty Measurer $+$ + Training Scheduler and further categorize the methodologies for automatic CL into four groups, i.e., Self-paced Learning, Transfer Teacher, RL Teacher, and Other Automatic CL. We also analyze principles to select different CL designs that may benefit practical applications. Finally, we present our insights on the relationships connecting CL and other machine learning concepts including transfer learning, meta-learning, continual learning and active learning, etc., then point out challenges in CL as well as potential future research directions deserving further investigations. [ABSTRACT FROM AUTHOR]

When demonstrating the effectiveness of a new algorithm, researchers are traditionally encouraged to compare their algorithm's performance against existing algorithms on well-studied benchmark test suites. In the absence of more nuanced methodologies, algorithm performance is typically summarized on average across the test suite examples. This paper highlights the potential bias of conclusions drawn by analyzing “on average” performance, and the opportunities offered by a recent testing methodology known as instance space analysis. To illustrate, we revisit our 2007 comparative study of algorithms for facial age estimation, and rigorously stress-test to challenge the original conclusions. The case study demonstrates how powerful visualizations offered by instance space analysis enable greater insights into unique strengths and weaknesses, and which algorithm should be used when and why. Inspired by such insights, a new algorithm is proposed, and its unique advantage is demonstrated. The bias often hidden in well-studied datasets, and the ramifications for drawing biased conclusions, are also illustrated in this case study. While focused on facial age estimation, the methodology and lessons learned from the case study are broadly applicable to any study seeking to draw conclusions about algorithm performance based on empirical results. [ABSTRACT FROM AUTHOR]

Deep learning is recognized to be capable of discovering deep features for representation learning and pattern recognition without requiring elegant feature engineering techniques by taking advantages of human ingenuity and prior knowledge. Thus it has triggered enormous research activities in machine learning and pattern recognition. One of the most important challenges of deep learning is to figure out relations between a feature and the depth of deep neural networks (deep nets for short) to reflect the necessity of depth. Our purpose is to quantify this feature-depth correspondence in feature extraction and generalization. We present the adaptivity of features to depths and vice-verse via showing a depth-parameter trade-off in extracting both single feature and composite features. Based on these results, we prove that implementing the classical empirical risk minimization on deep nets can achieve the optimal generalization performance for numerous learning tasks. Our theoretical results are verified by a series of numerical experiments including toy simulations and a real application of earthquake seismic intensity prediction. [ABSTRACT FROM AUTHOR]

Automated machine learning (AutoML) seeks to automatically find so-called machine learning pipelines that maximize the prediction performance when being used to train a model on a given dataset. One of the main and yet open challenges in AutoMLis an effective use of computational resources: An AutoML process involves the evaluation of many candidate pipelines, which are costly but often ineffective because they are canceled due to a timeout. In this paper, we present an approach to predict the runtime of two-step machine learning pipelines with up to one pre-processor, which can be used to anticipate whether or not a pipeline will time out. Separate runtime models are trained offline for each algorithm that may be used in a pipeline, and an overall prediction is derived from these models. We empirically show that the approach increases successful evaluations made by an AutoML tool while preserving or even improving on the previously best solutions. [ABSTRACT FROM AUTHOR]

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the joint embedding method identifies a linear subspace spanned by rank one symmetric matrices and projects adjacency matrices of graphs into this subspace. The projection coefficients can be treated as features of the graphs, while the embedding components can represent vertex features. We also propose a random graph model for multiple graphs that generalizes other classical models for graphs. We show through theory and numerical experiments that under the model, the joint embedding method produces estimates of parameters with small errors. Via simulation experiments, we demonstrate that the joint embedding method produces features which lead to state of the art performance in classifying graphs. Applying the joint embedding method to human brain graphs, we find it extracts interpretable features with good prediction accuracy in different tasks. [ABSTRACT FROM AUTHOR]

SafePredict is a novel meta-algorithm that works with any base prediction algorithm for online data to guarantee an arbitrarily chosen correctness rate, $1-\epsilon$ 1 - ε , by allowing refusals. Allowing refusals means that the meta-algorithm may refuse to emit a prediction produced by the base algorithm so that the error rate on non-refused predictions does not exceed $\epsilon$ ε . The SafePredict error bound does not rely on any assumptions on the data distribution or the base predictor. When the base predictor happens not to exceed the target error rate $\epsilon$ ε , SafePredict refuses only a finite number of times. When the error rate of the base predictor changes through time SafePredict makes use of a weight-shifting heuristic that adapts to these changes without knowing when the changes occur yet still maintains the correctness guarantee. Empirical results show that (i) SafePredict compares favorably with state-of-the-art confidence-based refusal mechanisms which fail to offer robust error guarantees; and (ii) combining SafePredict with such refusal mechanisms can in many cases further reduce the number of refusals. Our software is included in the supplementary material, which can be found on the Computer Society Digital Library at http://doi.ieeecomputersociety.org/10.1109/TPAMI.2019.2932415. [ABSTRACT FROM AUTHOR]

This work studies the problem of learning appropriate low dimensional image representations. We propose a generic algorithmic framework, which leverages two classic representation learning paradigms, i.e., sparse representation and the trace quotient criterion, to disentangle underlying factors of variation in high dimensional images. Specifically, we aim to learn simple representations of low dimensional, discriminant factors by applying the trace quotient criterion to well-engineered sparse representations. We construct a unified cost function, coined as the SPARse LOW dimensional representation (SparLow) function, for jointly learning both a sparsifying dictionary and a dimensionality reduction transformation. The SparLow function is widely applicable for developing various algorithms in three classic machine learning scenarios, namely, unsupervised, supervised, and semi-supervised learning. In order to develop efficient joint learning algorithms for maximizing the SparLow function, we deploy a framework of sparse coding with appropriate convex priors to ensure the sparse representations to be locally differentiable. Moreover, we develop an efficient geometric conjugate gradient algorithm to maximize the SparLow function on its underlying Riemannian manifold. Performance of the proposed SparLow algorithmic framework is investigated on several image processing tasks, such as 3D data visualization, face/digit recognition, and object/scene categorization. [ABSTRACT FROM AUTHOR]

For many computer vision and machine learning problems, large training sets are key for good performance. However, the most computationally expensive part of many computer vision and machine learning algorithms consists of finding nearest neighbor matches to high dimensional vectors that represent the training data. We propose new algorithms for approximate nearest neighbor matching and evaluate and compare them with previous algorithms. For matching high dimensional features, we find two algorithms to be the most efficient: the randomized k-d forest and a new algorithm proposed in this paper, the priority search k-means tree. We also propose a new algorithm for matching binary features by searching multiple hierarchical clustering trees and show it outperforms methods typically used in the literature. We show that the optimal nearest neighbor algorithm and its parameters depend on the data set characteristics and describe an automated configuration procedure for finding the best algorithm to search a particular data set. In order to scale to very large data sets that would otherwise not fit in the memory of a single machine, we propose a distributed nearest neighbor matching framework that can be used with any of the algorithms described in the paper. All this research has been released as an open source library called fast library for approximate nearest neighbors (FLANN), which has been incorporated into OpenCV and is now one of the most popular libraries for nearest neighbor matching. [ABSTRACT FROM AUTHOR]