We introduce normalized nonnegative models (NNM) for explorative data analysis. NNMs are partial convexifications of models from probability theory. We demonstrate their value at the example of item recommendation. We show that NNM-based recommender systems satisfy three criteria that all recommender systems should ideally satisfy: high predictive power, computational tractability, and expressive representations of users and items. Expressive user and item representations are important in practice to succinctly summarize the pool of customers and the pool of items. In NNMs, user representations are expressive because each user's preference can be regarded as normalized mixture of preferences of stereotypical users. The interpretability of item and user representations allow us to arrange properties of items (e.g., genres of movies or topics of documents) or users (e.g., personality traits) hierarchically.
These new interpretations of @math and @math allow us to deal with situations where @math is a categorical random variable and we can extract hierarchical structures from NNMs in a straightforward manner. Aspect models can deal with both of these tasks too. However, we think that dealing with these tasks in terms of aspect models is less natural then dealing with these tasks with NNMs. For instance, to model multiple outcomes like ( @math ) we need to first decide on a particular graphical model (see section 2.3 in @cite_3 ). Moreover, to extract hierarchical classifications of topics, we need to imagine generative processes like the nested Chinese restaurant process @cite_5 , or we need to employ nested hierarchical Dirichlet processes @cite_8 .
@cite_5 @cite_3 @cite_8
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We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP generalizes the nested Chinese restaurant process (nCRP) to allow each word to follow its own path to a topic node according to a per-document distribution over the paths on a shared tree. This alleviates the rigid, single-path formulation assumed by the nCRP, allowing documents to easily express complex thematic borrowings. We derive a stochastic variational inference algorithm for the model, which enables efficient inference for massive collections of text documents. We demonstrate our algorithm on 1.8 million documents from The New York Times and 2.7 million documents from Wikipedia . Inspired by a two-level theory from political science that unifies agenda setting and ideological framing, we propose supervised hierarchical latent Dirichlet allocation (SHLDA), which jointly captures documents' multi-level topic structure and their polar response variables. Our model extends the nested Chinese restaurant processes to discover tree-structured topic hierarchies and uses both per-topic hierarchical and per-word lexical regression parameters to model response variables. SHLDA improves prediction on political affiliation and sentiment tasks in addition to providing insight into how topics under discussion are framed. We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting—which of the large collection of possible trees to use? We take a Bayesian approach, generating an appropriate prior via a distribution on partitions that we refer to as the nested Chinese restaurant process. This nonparametric prior allows arbitrarily large branching factors and readily accommodates growing data collections. We build a hierarchical topic model by combining this prior with a likelihood that is based on a hierarchical variant of latent Dirichlet allocation. We illustrate our approach on simulated data and with an application to the modeling of NIPS abstracts. To help users quickly understand the major opinions from massive online reviews, it is important to automatically reveal the latent structure of the aspects, sentiment polarities, and the association between them. However, there is little work available to do this effectively. In this paper, we propose a hierarchical aspect sentiment model (HASM) to discover a hierarchical structure of aspect-based sentiments from unlabeled online reviews. In HASM, the whole structure is a tree. Each node itself is a two-level tree, whose root represents an aspect and the children represent the sentiment polarities associated with it. Each aspect or sentiment polarity is modeled as a distribution of words. To automatically extract both the structure and parameters of the tree, we use a Bayesian nonparametric model, recursive Chinese Restaurant Process (rCRP), as the prior and jointly infer the aspect-sentiment tree from the review texts. Experiments on two real datasets show that our model is comparable to two other hierarchical topic models in terms of quantitative measures of topic trees. It is also shown that our model achieves better sentence-level classification accuracy than previously proposed aspect-sentiment joint models. Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the regularization by the @math -norm. In this paper, we consider situations where we are not only interested in sparsity, but where some structural prior knowledge is available as well. We show that the @math -norm can then be extended to structured norms built on either disjoint or overlapping groups of variables, leading to a flexible framework that can deal with various structures. We present applications to unsupervised learning, for structured sparse principal component analysis and hierarchical dictionary learning, and to supervised learning in the context of non-linear variable selection. With the availability of cheap location sensors, geotagging of messages in online social networks is proliferating. For instance, Twitter, Facebook, Foursquare, and Google+ provide these services both explicitly by letting users choose their location or implicitly via a sensor. This paper presents an integrated generative model of location and message content. That is, we provide a model for combining distributions over locations, topics, and over user characteristics, both in terms of location and in terms of their content preferences. Unlike previous work which modeled data in a flat pre-defined representation, our model automatically infers both the hierarchical structure over content and over the size and position of geographical locations. This affords significantly higher accuracy --- location uncertainty is reduced by 40 relative to the best previous results [21] achieved on location estimation from Tweets. We achieve this goal by proposing a new statistical model, the nested Chinese Restaurant Franchise (nCRF), a hierarchical model of tree distributions. Much statistical structure is shared between users. That said, each user has his own distribution over interests and places. The use of the nCRF allows us to capture the following effects: (1) We provide a topic model for Tweets; (2) We obtain location specific topics; (3) We infer a latent distribution of locations; (4) We provide a joint hierarchical model of topics and locations; (5) We infer personalized preferences over topics and locations within the above model. In doing so, we are both able to obtain accurate estimates of the location of a user based on his tweets and to obtain a detailed estimate of a geographical language model. We define the hierarchical singular value decomposition (SVD) for tensors of order @math . This hierarchical SVD has properties like the matrix SVD (and collapses to the SVD in @math ), and we prove these. In particular, one can find low rank (almost) best approximations in a hierarchical format ( @math -Tucker) which requires only @math parameters, where @math is the order of the tensor, @math the size of the modes, and @math the (hierarchical) rank. The @math -Tucker format is a specialization of the Tucker format and it contains as a special case all (canonical) rank @math tensors. Based on this new concept of a hierarchical SVD we present algorithms for hierarchical tensor calculations allowing for a rigorous error analysis. The complexity of the truncation (finding lower rank approximations to hierarchical rank @math tensors) is in @math and the attainable accuracy is just 2-3 digits less than machine precision. We introduce normalized nonnegative models (NNM) for explorative data analysis. NNMs are partial convexifications of models from probability theory. We demonstrate their value at the example of item recommendation. We show that NNM-based recommender systems satisfy three criteria that all recommender systems should ideally satisfy: high predictive power, computational tractability, and expressive representations of users and items. Expressive user and item representations are important in practice to succinctly summarize the pool of customers and the pool of items. In NNMs, user representations are expressive because each user's preference can be regarded as normalized mixture of preferences of stereotypical users. The interpretability of item and user representations allow us to arrange properties of items (e.g., genres of movies or topics of documents) or users (e.g., personality traits) hierarchically. Emotional state recognition has become an important topic for human-robot interaction in the past years. By determining emotion expressions, robots can identify important variables of human behavior and use these to communicate in a more human-like fashion and thereby extend the interaction possibilities. Human emotions are multimodal and spontaneous, which makes them hard to be recognized by robots. Each modality has its own restrictions and constraints which, together with the non-structured behavior of spontaneous expressions, create several difficulties for the approaches present in the literature, which are based on several explicit feature extraction techniques and manual modality fusion. Our model uses a hierarchical feature representation to deal with spontaneous emotions, and learns how to integrate multiple modalities for non-verbal emotion recognition, making it suitable to be used in an HRI scenario. Our experiments show that a significant improvement of recognition accuracy is achieved when we use hierarchical features and multimodal information, and our model improves the accuracy of state-of-the-art approaches from 82.5 reported in the literature to 91.3 for a benchmark dataset on spontaneous emotion expressions. Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. We consider two competing first passage percolation processes started from uniformly chosen subsets of a random regular graph on @math vertices. The processes are allowed to spread with different rates, start from vertex subsets of different sizes or at different times. We obtain tight results regarding the sizes of the vertex sets occupied by each process, showing that in the generic situation one process will occupy @math vertices, for some @math . The value of @math is calculated in terms of the relative rates of the processes, as well as the sizes of the initial vertex sets and the possible time advantage of one process. The motivation for this work comes from the study of viral marketing on social networks. The described processes can be viewed as two competing products spreading through a social network (random regular graph). Considering the processes which grow at different rates (corresponding to different attraction levels of the two products) or starting at different times (the first to market advantage) allows to model aspects of real competition. The results obtained can be interpreted as one of the two products taking the lion share of the market. We compare these results to the same process run on @math dimensional grids where we show that in the generic situation the two products will have a linear fraction of the market each. We consider the problem of scheduling n independent jobs on m parallel machines, where the machines differ in their functionality but not in their processing speeds. Each job has a restricted set of machines to which it can be assigned, called its processing set. Preemption is not allowed. Our goal is to minimize the makespan of the schedule. We study two variants of this problem: (1) the case of tree-hierarchical processing set and (2) the case of nested processing set. We first give a fast algorithm for the case of tree-hierarchical processing set with a worst-case bound of 4 3, which is better than the best known algorithm whose worst-case bound is 2. We then give a more complicated algorithm for the case of nested processing set with a worst-case bound of 5 3, which is better than the best known algorithm whose worst-case bound is 7 4. In both cases, we will give examples achieving the worst-case bounds. Identifying expansion forms for acronyms is beneficial to many natural language processing and information retrieval tasks. In this work, we study the problem of finding expansions in texts for given acronym queries by modeling the problem as a sequence labeling task. However, it is challenging for traditional sequence labeling models like Conditional Random Fields (CRF) due to the complexity of the input sentences and the substructure of the categories. In this paper, we propose a Latent-state Neural Conditional Random Fields model (LNCRF) to deal with the challenges. On one hand, we extend CRF by coupling it with nonlinear hidden layers to learn multi-granularity hierarchical representations of the input data under the framework of Conditional Random Fields. On the other hand, we introduce latent variables to capture the fine granular information from the intrinsic substructures within the structured output labels implicitly. The experimental results on real data show that our model achieves the best performance against the state-of-the-art baselines. We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of “components.” Typically, these components are linear combinations of the rows and columns of the matrix, and are thus difficult to interpret in terms of the original features of the input data. In this paper, we propose and study matrix approximations that are explicitly expressed in terms of a small number of columns and or rows of the data matrix, and thereby more amenable to interpretation in terms of the original data. Our main algorithmic results are two randomized algorithms which take as input an @math matrix @math and a rank parameter @math . In our first algorithm, @math is chosen, and we let @math , where @math is the Moore-Penrose generalized inverse of @math . In our second algorithm @math , @math , @math are chosen, and we let @math . ( @math and @math are matrices that consist of actual columns and rows, respectively, of @math , and @math is a generalized inverse of their intersection.) For each algorithm, we show that with probability at least @math , @math , where @math is the “best” rank- @math approximation provided by truncating the SVD of @math , and where @math is the Frobenius norm of the matrix @math . The number of columns of @math and rows of @math is a low-degree polynomial in @math , @math , and @math . Both the Numerical Linear Algebra community and the Theoretical Computer Science community have studied variants of these matrix decompositions over the last ten years. However, our two algorithms are the first polynomial time algorithms for such low-rank matrix approximations that come with relative-error guarantees; previously, in some cases, it was not even known whether such matrix decompositions exist. Both of our algorithms are simple and they take time of the order needed to approximately compute the top @math singular vectors of @math . The technical crux of our analysis is a novel, intuitive sampling method we introduce in this paper called “subspace sampling.” In subspace sampling, the sampling probabilities depend on the Euclidean norms of the rows of the top singular vectors. This allows us to obtain provable relative-error guarantees by deconvoluting “subspace” information and “size-of- @math ” information in the input matrix. This technique is likely to be useful for other matrix approximation and data analysis problems. The celebrated Time Hierarchy Theorem for Turing machines states, informally, that more problems can be solved given more time. The extent to which a time hierarchy-type theorem holds in the distributed LOCAL model has been open for many years. It is consistent with previous results that all natural problems in the LOCAL model can be classified according to a small constant number of complexities, such as @math , etc. In this paper we establish the first time hierarchy theorem for the LOCAL model and prove that several gaps exist in the LOCAL time hierarchy. 1. We define an infinite set of simple coloring problems called Hierarchical @math -Coloring . A correctly colored graph can be confirmed by simply checking the neighborhood of each vertex, so this problem fits into the class of locally checkable labeling (LCL) problems. However, the complexity of the @math -level Hierarchical @math -Coloring problem is @math , for @math . The upper and lower bounds hold for both general graphs and trees, and for both randomized and deterministic algorithms. 2. Consider any LCL problem on bounded degree trees. We prove an automatic-speedup theorem that states that any randomized @math -time algorithm solving the LCL can be transformed into a deterministic @math -time algorithm. Together with a previous result, this establishes that on trees, there are no natural deterministic complexities in the ranges @math --- @math or @math --- @math . 3. We expose a gap in the randomized time hierarchy on general graphs. Any randomized algorithm that solves an LCL problem in sublogarithmic time can be sped up to run in @math time, which is the complexity of the distributed Lovasz local lemma problem, currently known to be @math and @math . Process mining refers to the extraction of process models from event logs. Real-life processes tend to be less structured and more flexible. Traditional process mining algorithms have problems dealing with such unstructured processes and generate spaghetti-like process models that are hard to comprehend. One reason for such a result can be attributed to constructing process models from raw traces without due pre-processing. In an event log, there can be instances where the system is subjected to similar execution patterns behavior. Discovery of common patterns of invocation of activities in traces (beyond the immediate succession relation) can help in improving the discovery of process models and can assist in defining the conceptual relationship between the tasks activities. In this paper, we characterize and explore the manifestation of commonly used process model constructs in the event log and adopt pattern definitions that capture these manifestations, and propose a means to form abstractions over these patterns. We also propose an iterative method of transformation of traces which can be applied as a pre-processing step for most of today's process mining techniques . The proposed approaches are shown to identify promising patterns and conceptually-valid abstractions on a real-life log. The patterns discussed in this paper have multiple applications such as trace clustering, fault diagnosis anomaly detection besides being an enabler for hierarchical process discovery. This paper presents a new approach for learning in structured domains (SDs) using a constructive neural network for graphs (NN4G). The new model allows the extension of the input domain for supervised neural networks to a general class of graphs including both acyclic cyclic, directed undirected labeled graphs. In particular, the model can realize adaptive contextual transductions, learning the mapping from graphs for both classification and regression tasks. In contrast to previous neural networks for structures that had a recursive dynamics, NN4G is based on a constructive feedforward architecture with state variables that uses neurons with no feedback connections. The neurons are applied to the input graphs by a general traversal process that relaxes the constraints of previous approaches derived by the causality assumption over hierarchical input data. Moreover, the incremental approach eliminates the need to introduce cyclic dependencies in the definition of the system state variables. In the traversal process, the NN4G units exploit (local) contextual information of the graphs vertices. In spite of the simplicity of the approach, we show that, through the compositionality of the contextual information developed by the learning, the model can deal with contextual information that is incrementally extended according to the graphs topology. The effectiveness and the generality of the new approach are investigated by analyzing its theoretical properties and providing experimental results. Natural language interfaces are powerful tools that enables humans and robots to convey information without the need for extensive training or complex graphical interfaces. Statistical techniques that employ probabilistic graphical models have proven effective at interpreting symbols that represent commands and observations for robot direction-following and object manipulation. A limitation of these approaches is their inefficiency in dealing with larger and more complex symbolic representations. Herein, we present a model for language understanding that uses parse trees and environment models both to learn the structure of probabilistic graphical models and to perform inference over this learned structure for symbol grounding. This model, called the Hierarchical Distributed Correspondence Graph (HDCG), exploits information about symbols that are expressed in the corpus to construct minimalist graphical models that are more efficient to search. In a series of comparative experiments, we demonstrate a significant improvement in efficiency without loss in accuracy over contemporary approaches for human-robot interaction. Deep neural networks (DNNs) have begun to have a pervasive impact on various applications of machine learning. However, the problem of finding an optimal DNN architecture for large applications is challenging. Common approaches go for deeper and larger DNN architectures but may incur substantial redundancy. To address these problems, we introduce a network growth algorithm that complements network pruning to learn both weights and compact DNN architectures during training. We propose a DNN synthesis tool (NeST) that combines both methods to automate the generation of compact and accurate DNNs. NeST starts with a randomly initialized sparse network called the seed architecture. It iteratively tunes the architecture with gradient-based growth and magnitude-based pruning of neurons and connections. Our experimental results show that NeST yields accurate, yet very compact DNNs, with a wide range of seed architecture selection. For the LeNet-300-100 (LeNet-5) architecture, we reduce network parameters by @math 70.2× ( @math 74.3×) and floating-point operations (FLOPs) by @math 79.4× ( @math 43.7×). For the AlexNet, VGG-16, and ResNet-50 architectures, we reduce network parameters (FLOPs) by @math 15.7× ( @math 4.6×), @math 33.2× ( @math 8.9×), and @math 4.1× ( @math 2.1×) respectively. NeST's grow-and-prune paradigm delivers significant additional parameter and FLOPs reduction relative to pruning-only methods.