We present a supervised-learning algorithm from graph data (a set of graphs) for arbitrary twice-differentiable loss functions and sparse linear models over all possible subgraph features. To date, it has been shown that under all possible subgraph features, several types of sparse learning, such as Adaboost, LPBoost, LARS LASSO, and sparse PLS regression, can be performed. Particularly emphasis is placed on simultaneous learning of relevant features from an infinite set of candidates. We first generalize techniques used in all these preceding studies to derive an unifying bounding technique for arbitrary separable functions. We then carefully use this bounding to make block coordinate gradient descent feasible over infinite subgraph features, resulting in a fast converging algorithm that can solve a wider class of sparse learning problems over graph data. We also empirically study the differences from the existing approaches in convergence property, selected subgraph features, and search-space sizes. We further discuss several unnoticed issues in sparse learning over all possible subgraph features.
These two existing, popular approaches are based on subgraph features, which are limited to specific type ones only. In contrast, a series of inspiring studies for has been made . These approaches involve automatic selection of relevant features from during the learning process. Triggered by the seminal paper by @cite_2 , it has been shown that we can perform simultaneous learning of not only the model parameters but also relevant subgraph features from all possible subgraphs in several machine-learning problems such as Adaboost , LARS LASSO , sparse partial-least-squares (PLS) regression , sparse principal component analysis (PCA) , and LPBoost . This paper aims to give a coherent and unifying view to understand how these existing methods work well, and then present a more general framework, which is applicable to a wider class of learning problems.
@cite_2
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Topic models, such as Latent Dirichlet Allocation (LDA), posit that documents are drawn from admixtures of distributions over words, known as topics. The inference problem of recovering topics from admixtures, is NP-hard. Assuming separability, a strong assumption, [4] gave the first provable algorithm for inference. For LDA model, [6] gave a provable algorithm using tensor-methods. But [4,6] do not learn topic vectors with bounded @math error (a natural measure for probability vectors). Our aim is to develop a model which makes intuitive and empirically supported assumptions and to design an algorithm with natural, simple components such as SVD, which provably solves the inference problem for the model with bounded @math error. A topic in LDA and other models is essentially characterized by a group of co-occurring words. Motivated by this, we introduce topic specific Catchwords, group of words which occur with strictly greater frequency in a topic than any other topic individually and are required to have high frequency together rather than individually. A major contribution of the paper is to show that under this more realistic assumption, which is empirically verified on real corpora, a singular value decomposition (SVD) based algorithm with a crucial pre-processing step of thresholding, can provably recover the topics from a collection of documents drawn from Dominant admixtures. Dominant admixtures are convex combination of distributions in which one distribution has a significantly higher contribution than others. Apart from the simplicity of the algorithm, the sample complexity has near optimal dependence on @math , the lowest probability that a topic is dominant, and is better than [4]. Empirical evidence shows that on several real world corpora, both Catchwords and Dominant admixture assumptions hold and the proposed algorithm substantially outperforms the state of the art [5]. This paper exploits the discriminative power of manifold learning in conjunction with the parsimonious power of sparse signal representation to perform robust facial expression recognition. By utilizing an l1 reconstruction error and a statistical mixture model, both accuracy and tolerance to occlusion improve without the need to perform neutral frame subtraction. Initially facial features are mapped onto a low dimensional manifold using supervised Locality Preserving Projections. Then an l1 optimization is employed to relate surface projections to training exemplars, where reconstruction models on facial regions determine the expression class. Experimental procedures and results are done in accordance with the recently published extended Cohn-Kanade and GEMEP-FERA datasets. Results demonstrate that posed datasets overemphasize the mouth region, while spontaneous datasets rely more on the upper cheek and eye regions. Despite these differences, the proposed method overcomes previous limitations to using sparse methods for facial expression and produces state-of-the-art results on both types of datasets. Despite the availability of a huge amount of video data accompanied by descriptive texts, it is not always easy to exploit the information contained in natural language in order to automatically recognize video concepts. Towards this goal, in this paper we use textual cues as means of supervision, introducing two weakly supervised techniques that extend the Multiple Instance Learning (MIL) framework: the Fuzzy Sets Multiple Instance Learning (FSMIL) and the Probabilistic Labels Multiple Instance Learning (PLMIL). The former encodes the spatio-temporal imprecision of the linguistic descriptions with Fuzzy Sets, while the latter models different interpretations of each description's semantics with Probabilistic Labels, both formulated through a convex optimization algorithm. In addition, we provide a novel technique to extract weak labels in the presence of complex semantics, that consists of semantic similarity computations. We evaluate our methods on two distinct problems, namely face and action recognition, in the challenging and realistic setting of movies accompanied by their screenplays, contained in the COGNIMUSE database. We show that, on both tasks, our method considerably outperforms a state-of-the-art weakly supervised approach, as well as other baselines. In this paper, we propose a new active learning algorithm in which the learner chooses the samples to be queried from the unlabeled data points whose attributes are only partially observed. In addition, we propose a cost-driven decision framework where the learner chooses to query either the labels or the missing attributes. This problem statement addresses a common constraint when building large datasets and applying active learning techniques on them, where some of the attributes (including the labels) are significantly harder or more costly to acquire per data point. We take a novel approach to this problem, first by building an imputation model that maps from the partially featured data to the fully featured dimension, and then performing active learning on the projected input space combined with the estimated confidence of inference. We discuss that our approach is flexible and can work with graph mining tasks as well as conventional semi-supervised learning problems. The results suggest that the proposed algorithm facilitates more cost-efficient annotation than the baselines. Machine learning research has, to a great extent, ignored an important aspect of many real world applications: time. Existing concept learners predominantly operate on a static set of attributes; for example, classifying flowers described by leaf size, pet al colour and pet al count. However, many real datasets are not static; they cannot sensibly be represented as a fixed set of attributes. Rather, the examples are expressed as features that vary temporally, and it is the temporal variation itself that is used for classification. Consider a simple gesture recognition domain, in which the temporal features are the position of the hands, finger bends, and so on. Looking at the position of the hand at one point in time is not likely to lead to a successful classification; it is only by analysing changes in position that recognition is possible. This thesis presents a new technique for temporal classification. By extracting sub-events from the training instances and parameterising them to allow feature construction for a subsequent learning process, it is able to employ background knowledge and express learnt concepts in terms of the background knowledge. The novel results of the thesis are: a temporal learner capable of producing comprehensible and accurate classifiers for multivariate time series that can learn from a small number of instances and can integrate non-temporal features; a feature construction technique that parameterises sub-events of the training set and clusters them to construct features for a propositional learner; and a technique for post-processing classification rules produced by the learner to give a comprehensible description expressed in the same form as the original background knowledge. The thesis discusses the implementation of TClass, a temporal learner. Results show rules that are comprehensible in many cases and accuracy results close to or better than existing technique—over 98 per cent for sign language and 72 per cent for ECGs (equivalent to the accuracy of a human cardiologist). One further surprising result is that a small set of very primitive sub-events proves to be functional, avoiding the need for labour-intensive background knowledge if it is not available. It is difficult to apply machine learning to new domains because often we lack labeled problem instances. In this paper, we provide a solution to this problem that leverages domain knowledge in the form of affinities between input features and classes. For example, in a baseball vs. hockey text classification problem, even without any labeled data, we know that the presence of the word puck is a strong indicator of hockey. We refer to this type of domain knowledge as a labeled feature. In this paper, we propose a method for training discriminative probabilistic models with labeled features and unlabeled instances. Unlike previous approaches that use labeled features to create labeled pseudo-instances, we use labeled features directly to constrain the model's predictions on unlabeled instances. We express these soft constraints using generalized expectation (GE) criteria --- terms in a parameter estimation objective function that express preferences on values of a model expectation. In this paper we train multinomial logistic regression models using GE criteria, but the method we develop is applicable to other discriminative probabilistic models. The complete objective function also includes a Gaussian prior on parameters, which encourages generalization by spreading parameter weight to unlabeled features. Experimental results on text classification data sets show that this method outperforms heuristic approaches to training classifiers with labeled features. Experiments with human annotators show that it is more beneficial to spend limited annotation time labeling features rather than labeling instances. For example, after only one minute of labeling features, we can achieve 80 accuracy on the ibm vs. mac text classification problem using GE-FL, whereas ten minutes labeling documents results in an accuracy of only 77 We propose a sparse-coding framework for activity recognition in ubiquitous and mobile computing that alleviates two fundamental problems of current supervised learning approaches. (i) It automatically derives a compact, sparse and meaningful feature representation of sensor data that does not rely on prior expert knowledge and generalizes well across domain boundaries. (ii) It exploits unlabeled sample data for bootstrapping effective activity recognizers, i.e., substantially reduces the amount of ground truth annotation required for model estimation. Such unlabeled data is easy to obtain, e.g., through contemporary smartphones carried by users as they go about their everyday activities.Based on the self-taught learning paradigm we automatically derive an over-complete set of basis vectors from unlabeled data that captures inherent patterns present within activity data. Through projecting raw sensor data onto the feature space defined by such over-complete sets of basis vectors effective feature extraction is pursued. Given these learned feature representations, classification backends are then trained using small amounts of labeled training data.We study the new approach in detail using two datasets which differ in terms of the recognition tasks and sensor modalities. Primarily we focus on a transportation mode analysis task, a popular task in mobile-phone based sensing. The sparse-coding framework demonstrates better performance than the state-of-the-art in supervised learning approaches. More importantly, we show the practical potential of the new approach by successfully evaluating its generalization capabilities across both domain and sensor modalities by considering the popular Opportunity dataset. Our feature learning approach outperforms state-of-the-art approaches to analyzing activities of daily living. Two problems arise when using distant supervision for relation extraction. First, in this method, an already existing knowledge base is heuristically aligned to texts, and the alignment results are treated as labeled data. However, the heuristic alignment can fail, resulting in wrong label problem. In addition, in previous approaches, statistical models have typically been applied to ad hoc features. The noise that originates from the feature extraction process can cause poor performance. In this paper, we propose a novel model dubbed the Piecewise Convolutional Neural Networks (PCNNs) with multi-instance learning to address these two problems. To solve the first problem, distant supervised relation extraction is treated as a multi-instance problem in which the uncertainty of instance labels is taken into account. To address the latter problem, we avoid feature engineering and instead adopt convolutional architecture with piecewise max pooling to automatically learn relevant features. Experiments show that our method is effective and outperforms several competitive baseline methods. The regularization principals [31] lead approximation schemes to deal with various learning problems, e.g., the regularization of the norm in a reproducing kernel Hilbert space for the ill-posed problem. In this paper, we present a family of subspace learning algorithms based on a new form of regularization, which transfers the knowledge gained in training samples to testing samples. In particular, the new regularization minimizes the Bregman divergence between the distribution of training samples and that of testing samples in the selected subspace, so it boosts the performance when training and testing samples are not independent and identically distributed. To test the effectiveness of the proposed regularization, we introduce it to popular subspace learning algorithms, e.g., principal components analysis (PCA) for cross-domain face modeling; and Fisher's linear discriminant analysis (FLDA), locality preserving projections (LPP), marginal Fisher's analysis (MFA), and discriminative locality alignment (DLA) for cross-domain face recognition and text categorization. Finally, we present experimental evidence on both face image data sets and text data sets, suggesting that the proposed Bregman divergence-based regularization is effective to deal with cross-domain learning problems. We consider the problem of learning a coefficient vector xο ∈ RN from noisy linear observation y = Axo + ∈ Rn. In many contexts (ranging from model selection to image processing), it is desirable to construct a sparse estimator x. In this case, a popular approach consists in solving an l1-penalized least-squares problem known as the LASSO or basis pursuit denoising. For sequences of matrices A of increasing dimensions, with independent Gaussian entries, we prove that the normalized risk of the LASSO converges to a limit, and we obtain an explicit expression for this limit. Our result is the first rigorous derivation of an explicit formula for the asymptotic mean square error of the LASSO for random instances. The proof technique is based on the analysis of AMP, a recently developed efficient algorithm, that is inspired from graphical model ideas. Simulations on real data matrices suggest that our results can be relevant in a broad array of practical applications. Learning visual representations with self-supervised learning has become popular in computer vision. The idea is to design auxiliary tasks where labels are free to obtain. Most of these tasks end up providing data to learn specific kinds of invariance useful for recognition. In this paper, we propose to exploit different self-supervised approaches to learn representations invariant to (i) inter-instance variations (two objects in the same class should have similar features) and (ii) intra-instance variations (viewpoint, pose, deformations, illumination, etc.). Instead of combining two approaches with multi-task learning, we argue to organize and reason the data with multiple variations. Specifically, we propose to generate a graph with millions of objects mined from hundreds of thousands of videos. The objects are connected by two types of edges which correspond to two types of invariance: “different instances but a similar viewpoint and category” and “different viewpoints of the same instance”. By applying simple transitivity on the graph with these edges, we can obtain pairs of images exhibiting richer visual invariance. We use this data to train a Triplet-Siamese network with VGG16 as the base architecture and apply the learned representations to different recognition tasks. For object detection, we achieve 63.2 mAP on PASCAL VOC 2007 using Fast R-CNN (compare to 67.3 with ImageNet pre-training). For the challenging COCO dataset, our method is surprisingly close (23.5 ) to the ImageNet-supervised counterpart (24.4 ) using the Faster R-CNN framework. We also show that our network can perform significantly better than the ImageNet network in the surface normal estimation task. Subspace learning techniques have been extensively used for dimensionality reduction (DR) in many pattern classification problem domains. Recently, methods like Subclass Discriminant Analysis (SDA) and Clustering-based Discriminant Analysis (CDA), which use subclass information for the discrimination between the data classes, have attracted much attention. In parallel, important work has been accomplished on Graph Embedding (GE), which is a general framework unifying several subspace learning techniques. In this paper, GE has been extended in order to integrate subclass discriminant information resulting to the novel Subclass Graph Embedding (SGE) framework, which is the main contribution of our work. It is proven that SGE encapsulates a diversity of both supervised and unsupervised unimodal methods like Locality Preserving Projections (LPP), Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). The theoretical link of SDA and CDA methods with SGE is also established. Along these lines, it is shown that SGE comprises a generalization of the typical GE framework including subclass DR methods. Moreover, it allows for an easy utilization of kernels for confronting non-linearly separable data. Employing SGE, in this paper a novel DR algorithm, which uses subclass discriminant information, called Subclass Marginal Fisher Analysis (SMFA) has been proposed. Through a series of experiments on various real-world datasets, it is shown that SMFA outperforms in most of the cases the state-of-the-art demonstrating the efficacy and power of SGE as a platform to develop new methods. HighlightsGraph Embedding is extended in order to integrate subclass informationThe novel Subclass Graph Embedding framework is proposed.The kernelized version of the new framework is presentedSubclass Graph Embedding encapsulates various subspace learning methods.A novel Subclass Marginal Fisher Analysis method is proposed. Summary Background—Most machine learning approaches only provide a classification for binary responses. However, probabilities are required for risk estimation using individual patient characteristics. It has been shown recently that every statistical learning machine known to be consistent for a nonparametric regression problem is a probability machine that is provably consistent for this estimation problem. Objectives—The aim of this paper is to show how random forests and nearest neighbors can be used for consistent estimation of individual probabilities. Methods—Two random forest algorithms and two nearest neighbor algorithms are described in detail for estimation of individual probabilities. We discuss the consistency of random forests, nearest neighbors and other learning machines in detail. We conduct a simulation study to illustrate the validity of the methods. We exemplify the algorithms by analyzing two well-known data sets on the diagnosis of appendicitis and the diagnosis of diabetes in Pima Indians. Results—Simulations demonstrate the validity of the method. With the real data application, we show the accuracy and practicality of this approach. We provide sample code from R packages in which the probability estimation is already available. This means that all calculations can be performed using existing software. Conclusions—Random forest algorithms as well as nearest neighbor approaches are valid machine learning methods for estimating individual probabilities for binary responses. Freely available implementations are available in R and may be used for applications. Abstract This paper proposes a unified approach to learning from constraints, which integrates the ability of classical machine learning techniques to learn from continuous feature-based representations with the ability of reasoning using higher-level semantic knowledge typical of Statistical Relational Learning. Learning tasks are modeled in the general framework of multi-objective optimization, where a set of constraints must be satisfied in addition to the traditional smoothness regularization term. The constraints translate First Order Logic formulas, which can express learning-from-example supervisions and general prior knowledge about the environment by using fuzzy logic. By enforcing the constraints also on the test set, this paper presents a natural extension of the framework to perform collective classification. Interestingly, the theory holds for both the case of data represented by feature vectors and the case of data simply expressed by pattern identifiers, thus extending classic kernel machines and graph regularization, respectively. This paper also proposes a probabilistic interpretation of the proposed learning scheme, and highlights intriguing connections with probabilistic approaches like Markov Logic Networks. Experimental results on classic benchmarks provide clear evidence of the remarkable improvements that are obtained with respect to related approaches. We address the pose mismatch problem which can occur in face verification systems that have only a single (frontal) face image available for training. In the framework of a Bayesian classifier based on mixtures of gaussians, the problem is tackled through extending each frontal face model with artificially synthesized models for non-frontal views. The synthesis methods are based on several implementations of maximum likelihood linear regression (MLLR), as well as standard multi-variate linear regression (LinReg). All synthesis techniques rely on prior information and learn how face models for the frontal view are related to face models for non-frontal views. The synthesis and extension approach is evaluated by applying it to two face verification systems: a holistic system (based on PCA-derived features) and a local feature system (based on DCT-derived features). Experiments on the FERET database suggest that for the holistic system, the LinReg-based technique is more suited than the MLLR-based techniques; for the local feature system, the results show that synthesis via a new MLLR implementation obtains better performance than synthesis based on traditional MLLR. The results further suggest that extending frontal models considerably reduces errors. It is also shown that the local feature system is less affected by view changes than the holistic system; this can be attributed to the parts based representation of the face, and, due to the classifier based on mixtures of gaussians, the lack of constraints on spatial relations between the face parts, allowing for deformations and movements of face areas. Learning visual representations with self-supervised learning has become popular in computer vision. The idea is to design auxiliary tasks where labels are free to obtain. Most of these tasks end up providing data to learn specific kinds of invariance useful for recognition. In this paper, we propose to exploit different self-supervised approaches to learn representations invariant to (i) inter-instance variations (two objects in the same class should have similar features) and (ii) intra-instance variations (viewpoint, pose, deformations, illumination, etc). Instead of combining two approaches with multi-task learning, we argue to organize and reason the data with multiple variations. Specifically, we propose to generate a graph with millions of objects mined from hundreds of thousands of videos. The objects are connected by two types of edges which correspond to two types of invariance: "different instances but a similar viewpoint and category" and "different viewpoints of the same instance". By applying simple transitivity on the graph with these edges, we can obtain pairs of images exhibiting richer visual invariance. We use this data to train a Triplet-Siamese network with VGG16 as the base architecture and apply the learned representations to different recognition tasks. For object detection, we achieve 63.2 mAP on PASCAL VOC 2007 using Fast R-CNN (compare to 67.3 with ImageNet pre-training). For the challenging COCO dataset, our method is surprisingly close (23.5 ) to the ImageNet-supervised counterpart (24.4 ) using the Faster R-CNN framework. We also show that our network can perform significantly better than the ImageNet network in the surface normal estimation task. We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlapping-group-lasso penalty, generalized from the group-lasso penalty; and (2) the graph-guided-fused-lasso penalty, generalized from the fused-lasso penalty. For both types of penalties, due to their nonseparability and nonsmoothness, developing an efficient optimization method remains a challenging problem. In this paper we propose a general optimization approach, the smoothing proximal gradient (SPG) method, which can solve structured sparse regression problems with any smooth convex loss under a wide spectrum of structured sparsity-inducing penalties. Our approach combines a smoothing technique with an effective proximal gradient method. It achieves a convergence rate significantly faster than the standard first-order methods, subgradient methods, and is much more scalable than the most widely used interior-point methods. The efficiency and scalability of our method are demonstrated on both simulation experiments and real genetic data sets. Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization problem by replacing the cardinality function by its convex envelope (tightest convex lower bound), in this case the L1-norm. In this paper, we investigate more general set-functions than the cardinality, that may incorporate prior knowledge or structural constraints which are common in many applications: namely, we show that for nondecreasing submodular set-functions, the corresponding convex envelope can be obtained from its extension, a common tool in submodular analysis. This defines a family of polyhedral norms, for which we provide generic algorithmic tools (subgradients and proximal operators) and theoretical results (conditions for support recovery or high-dimensional inference). By selecting specific submodular functions, we can give a new interpretation to known norms, such as those based on rank-statistics or grouped norms with potentially overlapping groups; we also define new norms, in particular ones that can be used as non-factorial priors for supervised learning. In this paper, we propose a very simple deep learning network for image classification that is based on very basic data processing components: 1) cascaded principal component analysis (PCA); 2) binary hashing; and 3) blockwise histograms. In the proposed architecture, the PCA is employed to learn multistage filter banks. This is followed by simple binary hashing and block histograms for indexing and pooling. This architecture is thus called the PCA network (PCANet) and can be extremely easily and efficiently designed and learned. For comparison and to provide a better understanding, we also introduce and study two simple variations of PCANet: 1) RandNet and 2) LDANet. They share the same topology as PCANet, but their cascaded filters are either randomly selected or learned from linear discriminant analysis. We have extensively tested these basic networks on many benchmark visual data sets for different tasks, including Labeled Faces in the Wild (LFW) for face verification; the MultiPIE, Extended Yale B, AR, Facial Recognition Technology (FERET) data sets for face recognition; and MNIST for hand-written digit recognition. Surprisingly, for all tasks, such a seemingly naive PCANet model is on par with the state-of-the-art features either prefixed, highly hand-crafted, or carefully learned [by deep neural networks (DNNs)]. Even more surprisingly, the model sets new records for many classification tasks on the Extended Yale B, AR, and FERET data sets and on MNIST variations. Additional experiments on other public data sets also demonstrate the potential of PCANet to serve as a simple but highly competitive baseline for texture classification and object recognition. Two machine learning approaches: mixture of experts and AdaBoost.R2 were adjusted to the real-world regression problem of predicting the prices of residential premises based on historical data of sales purchase transactions. The computationally intensive experiments were conducted aimed to compare empirically the prediction accuracy of ensemble models generated by the methods. The analysis of the results was performed using statistical methodology including nonparametric tests followed by post-hoc procedures designed especially for multiple n×n comparisons. No statistically significant differences were observed among the best ensembles: two generated by mixture of experts and two by AdaBoost.R2 employing multilayer perceptrons and general linear models as base learning algorithms.