We propose a principle for exploring context in machine learning models. Starting with a simple assumption that each observation may or may not depend on its context, a conditional probability distribution is decomposed into two parts: context-free and context-sensitive. Then by employing the log-linear word production model for relating random variables to their embedding space representation and making use of the convexity of natural exponential function, we show that the embedding of an observation can also be decomposed into a weighted sum of two vectors, representing its context-free and context-sensitive parts, respectively. This simple treatment of context provides a unified view of many existing deep learning models, leading to revisions of these models able to achieve significant performance boost. Specifically, our upgraded version of a recent sentence embedding model not only outperforms the original one by a large margin, but also leads to a new, principled approach for compositing the embeddings of bag-of-words features, as well as a new architecture for modeling attention in deep neural networks. More surprisingly, our new principle provides a novel understanding of the gates and equations defined by the long short term memory model, which also leads to a new model that is able to converge significantly faster and achieve much lower prediction errors. Furthermore, our principle also inspires a new type of generic neural network layer that better resembles real biological neurons than the traditional linear mapping plus nonlinear activation based architecture. Its multi-layer extension provides a new principle for deep neural networks which subsumes residual network (ResNet) as its special case, and its extension to convolutional neutral network model accounts for irrelevant input (e.g., background in an image) in addition to filtering.
In parallel to neural network based models, another popular approach to feature embedding is based on matrix factorization , where a column represents a feature (, a movie) and each row represents a cooccurrence of features (, list of movies watched by a user). In this setting, one can compute the embeddings for both the features and cooccurrences, and the embedding for a new cooccurring case (bag of features) can be computed in a closed form . Recently, the concept of cooccurrence is generalized to n-grams by reformulating the embeddings of bag-of-features as a compressed sensing problem @cite_10 . Nevertheless, these methods are mostly limited to linear systems with closed-form solutions.
@cite_10
2749348810 2792922843 2601789736 2752965000
Recently, many e-commerce websites have encouraged their users to rate shopping items and write review texts. This review information has been very useful for understanding user preferences and item properties, as well as enhancing the capability to make personalized recommendations of these websites. In this paper, we propose to model user preferences and item properties using convolutional neural networks (CNNs) with dual local and global attention, motivated by the superiority of CNNs to extract complex features. By using aggregated review texts from a user and aggregated review text for an item, our model can learn the unique features (embedding) of each user and each item. These features are then used to predict ratings. We train these user and item networks jointly which enable the interaction between users and items in a similar way as matrix factorization. The local attention provides us insight on a user's preferences or an item's properties. The global attention helps CNNs focus on the semantic meaning of the whole review text. Thus, the combined local and global attentions enable an interpretable and better-learned representation of users and items. We validate the proposed models by testing on popular review datasets in Yelp and Amazon and compare the results with matrix factorization (MF), the hidden factor and topical (HFT) model, and the recently proposed convolutional matrix factorization (ConvMF+). Our proposed CNNs with dual attention model outperforms HFT and ConvMF+ in terms of mean square errors (MSE). In addition, we compare the user item embeddings learned from these models for classification and recommendation. These results also confirm the superior quality of user item embeddings learned from our model. The mainstream direction in face alignment is now dominated by cascaded regression methods. These methods start from an image with an initial shape and build a set of shape increments based on features with respect to the current estimated shape. These shape increments move the initial shape to the desired location. Despite the advantages of the cascaded methods, they all share two major limitations: (i) shape increments are learned independently from each other in a cascaded manner, (ii) the use of standard generic computer vision features such SIFT, HOG, does not allow these methods to learn problem-specific features. In this work, we propose a novel Recurrent Convolutional Shape Regression (RCSR) method that overcomes these limitations. We formulate the standard cascaded alignment problem as a recurrent process and learn all shape increments jointly, by using a recurrent neural network with a gated recurrent unit. Importantly, by combining a convolutional neural network with a recurrent one we avoid hand-crafted features, widely adopted in the literature and thus we allow the model to learn task-specific features. Besides, we employ the convolutional gated recurrent unit which takes as input the feature tensors instead of flattened feature vectors. Therefore, the spatial structure of the features can be better preserved in the memory of the recurrent neural network. Moreover, both the convolutional and the recurrent neural networks are learned jointly. Experimental evaluation shows that the proposed method has better performance than the state-of-the-art methods, and further supports the importance of learning a single end-to-end model for face alignment. By stacking layers of convolution and nonlinearity, convolutional networks (ConvNets) effectively learn from lowlevel to high-level features and discriminative representations. Since the end goal of large-scale recognition is to delineate complex boundaries of thousands of classes, adequate exploration of feature distributions is important for realizing full potentials of ConvNets. However, state-of-theart works concentrate only on deeper or wider architecture design, while rarely exploring feature statistics higher than first-order. We take a step towards addressing this problem. Our method consists in covariance pooling, instead of the most commonly used first-order pooling, of highlevel convolutional features. The main challenges involved are robust covariance estimation given a small sample of large-dimensional features and usage of the manifold structure of covariance matrices. To address these challenges, we present a Matrix Power Normalized Covariance (MPNCOV) method. We develop forward and backward propagation formulas regarding the nonlinear matrix functions such that MPN-COV can be trained end-to-end. In addition, we analyze both qualitatively and quantitatively its advantage over the well-known Log-Euclidean metric. On the ImageNet 2012 validation set, by combining MPN-COV we achieve over 4 , 3 and 2.5 gains for AlexNet, VGG-M and VGG-16, respectively; integration of MPN-COV into 50-layer ResNet outperforms ResNet-101 and is comparable to ResNet-152. The source code will be available on the project page: http: www.peihuali.org MPN-COV. Recently, plugging trainable structural layers into deep convolutional neural networks (CNNs) as image representations has made promising progress. However, there has been little work on inserting parametric probability distributions, which can effectively model feature statistics, into deep CNNs in an end-to-end manner. This paper proposes a Global Gaussian Distribution embedding Network (G2DeNet) to take a step towards addressing this problem. The core of G2DeNet is a novel trainable layer of a global Gaussian as an image representation plugged into deep CNNs for end-to-end learning. The challenge is that the proposed layer involves Gaussian distributions whose space is not a linear space, which makes its forward and backward propagations be non-intuitive and non-trivial. To tackle this issue, we employ a Gaussian embedding strategy which respects the structures of both Riemannian manifold and smooth group of Gaussians. Based on this strategy, we construct the proposed global Gaussian embedding layer and decompose it into two sub-layers: the matrix partition sub-layer decoupling the mean vector and covariance matrix entangled in the embedding matrix, and the square-rooted, symmetric positive definite matrix sub-layer. In this way, we can derive the partial derivatives associated with the proposed structural layer and thus allow backpropagation of gradients. Experimental results on large scale region classification and fine-grained recognition tasks show that G2DeNet is superior to its counterparts, capable of achieving state-of-the-art performance.