Because of the ubiquitous applications of NMF, many efficient algorithms have been proposedforsolving(1).

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observedsamples isanNP-hard combinatorial problem. In this paper, we first show that for a set of important graph families it is possible toconvertthestructural constraints ofstructure intoeigenvalueconstraints ofthe graph Laplacianmatrix.

The authors present an intriguing take on factor analysis: namely, the use of Ganchev et al's posterior regularization to enforce non negativity constraints on the posterior. They present proofs of convergence and correctness, and present a scalable method for inference and learning in stacked constrained factor analysis models. The method appears to be sound and is an interesting direction overall, a refreshing departure from much of the existing literature, and the first instance of which I am aware that posterior regularization has been highlighted in a deep learning/unsupervised feature learning context. While I did not review it in detail, the degree of thoroughness demonstrated by the supplementary material is truly impressive. My main concern with this paper is one of being somewhat underwhelmed by the empirical evaluation, in light of the norms of the community.

The aim of this paper is to present an alternative formulation of the attention scoring function in translation tasks. Generally speaking, language is deeply structured, and this is reflected in the attention scoring matrix. We exploit this property to define the attention pooling function, taking this aspect into account. In the first chapters, we introduce the attention mechanism in mathematical terms and explain its limitations and alternative formulations. Next, we focus on the experimental session that led to the alternative formulation. Essentially, we guide queries and keys to interact in a specific manner, encoding the distinct roles of attention heads and directing values on where to seek context. In mathematical terms, we can think of this formula as projecting the attention scores matrix, say $H$, onto the space of band matrices with fixed bandwidth. This convex subspace is clearly finite-dimensional and therefore closed. As a consequence, the projection on this space is well-posed and unique. However, at the price of losing the uniqueness of the projection (i.e., the best approximation for $H$), we defined a new space consisting of band matrices plus error sparse matrices. We prove that this is a compact subspace which guarantees the existence of a matrix that best approximates $H$. We conclude the thesis by validating the new formula, namely calculating how well the new formula for attention scores approximates the original one. Additionally, we explore the impact of different parameters such as w (context windows) and num-pos (number of relevant words in a sentence). These analyses provide deeper insights into how languages are processed and translated, revealing nuances in the roles of context and word relevance.

We study the problem of segmenting specific white matter structures of interest from Diffusion Tensor (DT-MR) images of the human brain. This is an important requirement in many Neuroimaging studies: for instance, to evaluate whether a brain structure exhibits group level differences as a function of disease in a set of images. Typically, interactive expert guided segmentation has been the method of choice for such applications, but this is tedious for large datasets common today. To address this problem, we endow an image segmentation algorithm with'advice' encoding some global characteristics of the region(s) we want to extract. This is accomplished by constructing (using expert-segmented images) an epitome of a specific region - as a histogram over a bag of'words' (e.g.,suitable feature descriptors).

We study the problem of segmenting specific white matter structures of interest from Diffusion Tensor (DT-MR) images of the human brain. This is an important requirement in many Neuroimaging studies: for instance, to evaluate whether a brain structure exhibits group level differences as a function of disease in a set of images. Typically, interactive expert guided segmentation has been the method of choice for such applications, but this is tedious for large datasets common today. To address this problem, we endow an image segmentation algorithm with'advice' encoding some global characteristics of the region(s) we want to extract. This is accomplished by constructing (using expert-segmented images) an epitome of a specific region - as a histogram over a bag of'words' (e.g.,suitable feature descriptors).

We study worst-case bounds on the quality of any fixed point assignment of the max-product algorithm for Markov Random Fields (MRF). We start proving a bound independent of the MRF structure and parameters. Afterwards, we show how this bound can be improved for MRFs with particular structures such as bipartite graphs or grids. Our results provide interesting insight into the behavior of max-product. For example, we prove that max-product provides very good results (at least 90% of the optimal) on MRFs with large variable-disjoint cycles (MRFs in which all cycles are variable-disjoint, namely that they do not share any edge and in which each cycle contains at least 20 variables).

We study the problem of segmenting specific white matter structures of interest from Diffusion Tensor (DT-MR) images of the human brain. This is an important requirement in many Neuroimaging studies: for instance, to evaluate whether a brain structure exhibits group level differences as a function of disease in a set of images. Typically, interactive expert guided segmentation has been the method of choice for such applications, but this is tedious for large datasets common today. To address this problem, we endow an image segmentation algorithm with 'advice' encoding some global characteristics of the region(s) we want to extract. This is accomplished by constructing (using expert-segmented images) an epitome of a specific region - as a histogram over a bag of 'words' (e.g.,suitable feature descriptors). Now, given such a representation, the problem reduces to segmenting new brain image with additional constraints that enforce consistency between the segmented foreground and the pre-specified histogram over features. We present combinatorial approximation algorithms to incorporate such domain specific constraints for Markov Random Field (MRF) segmentation. Making use of recent results on image co-segmentation, we derive effective solution strategies for our problem. We provide an analysis of solution quality, and present promising experimental evidence showing that many structures of interest in Neuroscience can be extracted reliably from 3-D brain image volumes using our algorithm.