In this paper, we consider learning dictionary models over a network of agents, where each agent is only in charge of a portion of the dictionary elements. This formulation is relevant in Big Data scenarios where large dictionary models may be spread over different spatial locations and it is not feasible to aggregate all dictionaries in one location due to communication and privacy considerations. We first show that the dual function of the inference problem is an aggregation of individual cost functions associated with different agents, which can then be minimized efficiently by means of diffusion strategies. The collaborative inference step generates dual variables that are used by the agents to update their dictionaries without the need to share these dictionaries or even the coefficient models for the training data. This is a powerful property that leads to an effective distributed procedure for learning dictionaries over large networks (e.g., hundreds of agents in our experiments). Furthermore, the proposed learning strategy operates in an online manner and is able to respond to streaming data, where each data sample is presented to the network once.
With the increasing complexity of various learning tasks, it is not uncommon for the size of the learning dictionaries to be demanding in terms of memory and computing requirements. It is therefore important to study scenarios where the dictionary is not necessarily available in a single central location but its components are possibly spread out over multiple locations. This is particularly true in Big Data scenarios where large dictionary components may already be available at separate locations and it is not feasible to aggregate all dictionaries in one location due to communication and privacy considerations. This observation motivates us to examine how to learn a dictionary model that is stored over a network of agents, where each agent is in charge of only a portion of the dictionary elements. Compared with other works, the problem we solve in this article is how to learn a distributed dictionary model, which is, for example, different from the useful work in @cite_36 where it is assumed instead that each agent maintains the dictionary model.
@cite_36
2142940228 2086522948 114321176 2128870637
Algorithms for data-driven learning of domain-specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of Bayesian models with concave Schur-concave (CSC) negative log priors. Such priors are appropriate for obtaining sparse representations of environmental signals within an appropriately chosen (environmentally matched) dictionary. The elements of the dictionary can be interpreted as concepts, features, or words capable of succinct expression of events encountered in the environment (the source of the measured signals). This is a generalization of vector quantization in that one is interested in a description involving a few dictionary entries (the proverbial "25 words or less"), but not necessarily as succinct as one entry. To learn an environmentally adapted dictionary capable of concise expression of signals generated by the environment, we develop algorithms that iterate between a representative set of sparse representations found by variants of FOCUSS and an update of the dictionary using these sparse representations.Experiments were performed using synthetic data and natural images. For complete dictionaries, we demonstrate that our algorithms have improved performance over other independent component analysis (ICA) methods, measured in terms of signal-to-noise ratios of separated sources. In the overcomplete case, we show that the true underlying dictionary and sparse sources can be accurately recovered. In tests with natural images, learned overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries; that is, images encoded with an overcomplete dictionary have both higher compression (fewer bits per pixel) and higher accuracy (lower mean square error). By solving a linear inverse problem under a sparsity constraint, one can successfully recover the coefficients, if there exists such a sparse approximation for the proposed class of signals. In this framework the dictionary can be adapted to a given set of signals using dictionary learning methods. The learned dictionary often does not have useful structures for a fast implementation, i.e. fast matrix-vector multiplication. This prevents such a dictionary being used for the real applications or large scale problems. The structure can be induced on the dictionary throughout the learning progress. Examples of such structures are shift-invariance and being multi-scale. These dictionaries can be efficiently implemented using a filter bank. In this paper a well-known structure, called compressibility, is adapted to be used in the dictionary learning problem. As a result, the complexity of the implementation of a compressible dictionary can be reduced by wisely choosing a generative model. By some simulations, it has been shown that the learned dictionary provides sparser approximations, while it does not increase the computational complexity of the algorithms, with respect to the pre-designed fast structured dictionaries. An unsupervised iterative approach for extracting a new lexicon (or unknown words) from a Chinese text corpus is proposed in this paper. Instead of using a non-iterative segmentation-merging-filtering-and-disambiguation approach, the proposed method iteratively integrates the contextual constraints (among word candidates) and a joint character association metric to progressively improve the segmentation results of the input corpus (and thus the new word list.) An augmented dictionary, which includes potential unknown words (in addition to known words), is used to segment the input corpus, unlike traditional approaches which use only known words for segmentation. In the segmentation process, the augmented dictionary is used to impose contextual constraints over known words and potential unknown words within input sentences; an unsupervised Viterbi Training process is then applied to ensure that the selected potential unknown words (and known words) maximize the likelihood of the input corpus. On the other hand, the joint character association metric (which reflects the global character association characteristics across the corpus) is derived by integrating several commonly used word association metrics, such as mutual information and entropy, with a joint Gaussian mixture density function; such integration allows the filter to use multiple features simultaneously to evaluate character association, unlike traditional filters which apply multiple features independently. The proposed method then allows the contextual constraints and the joint character association metric to enhance each other; this is achieved by iteratively applying the joint association metric to truncate unlikely unknown words in the augmented dictionary and using the segmentation result to improve the estimation of the joint association metric. The refined augmented dictionary and improved estimation are then used in the next iteration to acquire better segmentation and carry out more reliable filtering. Experiments show that both the precision and recall rates are improved almost monotonically, in contrast to non-iterative segmentation-merging-filtering-and-disambiguation approaches, which often sacrifice precision for recall or vice versa. With a corpus of 311,591 sentences, the performance is 76 (bigram), 54 (trigram), and 70 (quadragram) in F-measure, which is significantly better than using the non-iterative approach with F-measures of 74 (bigram), 46 (trigram), and 58 (quadragram). Research into corpus-based semantics has focused on the development of ad hoc models that treat single tasks, or sets of closely related tasks, as unrelated challenges to be tackled by extracting different kinds of distributional information from the corpus. As an alternative to this "one task, one model" approach, the Distributional Memory framework extracts distributional information once and for all from the corpus, in the form of a set of weighted word-link-word tuples arranged into a third-order tensor. Different matrices are then generated from the tensor, and their rows and columns constitute natural spaces to deal with different semantic problems. In this way, the same distributional information can be shared across tasks such as modeling word similarity judgments, discovering synonyms, concept categorization, predicting selectional preferences of verbs, solving analogy problems, classifying relations between word pairs, harvesting qualia structures with patterns or example pairs, predicting the typical properties of concepts, and classifying verbs into alternation classes. Extensive empirical testing in all these domains shows that a Distributional Memory implementation performs competitively against task-specific algorithms recently reported in the literature for the same tasks, and against our implementations of several state-of-the-art methods. The Distributional Memory approach is thus shown to be tenable despite the constraints imposed by its multi-purpose nature.