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.