Logistic regression analysis of high-dimensional data, such as natural language text, poses computational and statistical challenges. Maximum likelihood estimation often fails in these applications. We present a simple Bayesian logistic regression approach that uses a Laplace prior to avoid overfitting and produces sparse predictive models for text data. We apply this approach to a range of doc...

virial theorem is important for understanding stellar structures. it produces an interesting connection between magnetic and gravitational energies. using the general form of the virial theorem including the magnetic field (toroidal magnetic field), we may explain the solar dynamo model in relation to variations of the magnetic and gravitational energies. we emphasize the role of the gravitatio...

In this thesis we study unsupervised learning algorithms for training feature extractors and building deep learning models. We propose sparse-modeling algorithms as the foundation for unsupervised feature extraction systems. To reduce the cost of the inference process required to obtain the optimal sparse code, we model a feed-forward function that is trained to predict this optimal sparse code...

Sparsity often leads to efficient and interpretable representations for data. In this paper, we introduce an architecture to infer the appropriate sparsity pattern for the word embeddings while learning the sentence composition in a deep network. The proposed approach produces competitive results in sentiment and topic classification tasks with high degree of sparsity. It is computationally che...

Force-directed layout methods constitute the most common approach to draw general graphs. Among them, stress minimization produces layouts of comparatively high quality but also imposes comparatively high computational demands. We propose a speed-up method based on the aggregation of terms in the objective function. It is akin to aggregate repulsion from far-away nodes during spring embedding b...

Several mathematical methods are discussed in this paper, which are applied in image compression and restoration. Singular value decomposition (SVD) is used in compressing image. Conjugate gradients (CG) method and truncated Singular value decomposition (TSVD) regularization method are applied in image restoration. From the experience results we can see that those methods are effective in image...