Explicit high-order feature interactions efficiently capture essential structural knowledge about the data of interest and have been used for constructing generative models. We present a supervised discriminative High-Order Parametric Embedding (HOPE) approach to data visualization and compression. Compared to deep embedding models with complicated deep architectures, HOPE generates more effective high-order feature mapping through an embarrassingly simple shallow model. Furthermore, two approaches to generating a small number of exemplars conveying high-order interactions to represent large-scale data sets are proposed. These exemplars in combination with the feature mapping learned by HOPE effectively capture essential data variations. Moreover, through HOPE, these exemplars are employed to increase the computational efficiency of kNN classification for fast information retrieval by thousands of times. For classification in two-dimensional embedding space on MNIST and USPS datasets, our shallow method HOPE with simple Sigmoid transformations significantly outperforms state-of-the-art supervised deep embedding models based on deep neural networks, and even achieved historically low test error rate of 0.65 in two-dimensional space on MNIST, which demonstrates the representational efficiency and power of supervised shallow models with high-order feature interactions.
High-order feature interactions have been studied for building more powerful generative models such as Boltzmann Machines and autoencoders @cite_8 @cite_11 @cite_17 @cite_4 @cite_21 . Factorization Machine (FM) @cite_19 and FHIM @cite_1 are similar to the version of HOPE with only linear projection, but they used feature interactions for classification, regression, or feature selection. None of previous research has been conducted under the context of data embedding, visualization, or compression, and therefore has different objective function or parametric form. Especially, our joint learning approach is completely different from previous methods. And to the best of our knowledge, our work here is the first successful one to model input feature interactions with order higher than two for practical supervised embedding.
@cite_4 @cite_8 @cite_21 @cite_1 @cite_17 @cite_19 @cite_11
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Identifying interpretable discriminative high-order feature interactions given limited training data in high dimensions is challenging in both machine learning and data mining. In this paper, we propose a factorization based sparse learning framework termed FHIM for identifying high-order feature interactions in linear and logistic regression models, and study several optimization methods for solving them. Unlike previous sparse learning methods, our model FHIM recovers both the main effects and the interaction terms accurately without imposing tree-structured hierarchical constraints. Furthermore, we show that FHIM has oracle properties when extended to generalized linear regression models with pairwise interactions. Experiments on simulated data show that FHIM outperforms the state-of-the-art sparse lear-ning techniques. Further experiments on our experimentally generated data from patient blood samples using a novel SOMAmer (Slow Off-rate Modified Aptamer) technology show that, FHIM performs blood-based cancer diagnosis and bio-marker discovery for Renal Cell Carcinoma much better than other competing methods, and it identifies interpretable block-wise high-order gene interactions predictive of cancer stages of samples. A literature survey shows that the interactions identified by FHIM play important roles in cancer development. Relation learning is a fundamental operation in many computer vision tasks. Recently, high-order Boltzmann machine and its variants have exhibited the great power of modelling various data relation. However, most of them are unsupervised learning models which are not very discriminative and thus cannot server as a standalone solution to relation learning tasks. In this paper, we explore supervised learning algorithms and propose a new model named Conditional High-order Boltzmann Machine (CHBM), which can be directly used as a bilinear classifier to assign similarity scores for pairwise images. Then, to better deal with complex data relation, we propose a gated version of CHBM which untangles factors of variation by exploiting a set of latent variables to gate classification. We perform four-order tensor factorization for parameter reduction, and present two efficient supervised learning algorithms from the perspectives of being generative and discriminative, respectively. The experimental results of image transformation visualization, binary-way classification and face verification demonstrate that, by performing supervised learning, our models can greatly improve the performance. Many predictive tasks of web applications need to model categorical variables, such as user IDs and demographics like genders and occupations. To apply standard machine learning techniques, these categorical predictors are always converted to a set of binary features via one-hot encoding, making the resultant feature vector highly sparse. To learn from such sparse data effectively, it is crucial to account for the interactions between features. Factorization Machines (FMs) are a popular solution for efficiently using the second-order feature interactions. However, FM models feature interactions in a linear way, which can be insufficient for capturing the non-linear and complex inherent structure of real-world data. While deep neural networks have recently been applied to learn non-linear feature interactions in industry, such as the Wide&Deep by Google and DeepCross by Microsoft, the deep structure meanwhile makes them difficult to train. In this paper, we propose a novel model Neural Factorization Machine (NFM) for prediction under sparse settings. NFM seamlessly combines the linearity of FM in modelling second-order feature interactions and the non-linearity of neural network in modelling higher-order feature interactions. Conceptually, NFM is more expressive than FM since FM can be seen as a special case of NFM without hidden layers. Empirical results on two regression tasks show that with one hidden layer only, NFM significantly outperforms FM with a 7.3 relative improvement. Compared to the recent deep learning methods Wide&Deep and DeepCross, our NFM uses a shallower structure but offers better performance, being much easier to train and tune in practice. Building intelligent systems that are capable of extracting high-level representations from high-dimensional sensory data lies at the core of solving many AI related tasks, including object recognition, speech perception, and language understanding. Theoretical and biological arguments strongly suggest that building such systems requires models with deep architectures that involve many layers of nonlinear processing. The aim of the thesis is to demonstrate that deep generative models that contain many layers of latent variables and millions of parameters can be learned efficiently, and that the learned high-level feature representations can be successfully applied in a wide spectrum of application domains, including visual object recognition, information retrieval, and classification and regression tasks. In addition, similar methods can be used for nonlinear dimensionality reduction. The first part of the thesis focuses on analysis and applications of probabilistic generative models called Deep Belief Networks. We show that these deep hierarchical models can learn useful feature representations from a large supply of unlabeled sensory inputs. The learned high-level representations capture a lot of structure in the input data, which is useful for subsequent problem-specific tasks, such as classification, regression or information retrieval, even though these tasks are unknown when the generative model is being trained. In the second part of the thesis, we introduce a new learning algorithm for a different type of hierarchical probabilistic model, which we call a Deep Boltzmann Machine. Like Deep Belief Networks, Deep Boltzmann Machines have the potential of learning internal representations that become increasingly complex at higher layers, which is a promising way of solving object and speech recognition problems. Unlike Deep Belief Networks and many existing models with deep architectures, the approximate inference procedure, in addition to a fast bottom-up pass, can incorporate top-down feedback. This allows Deep Boltzmann Machines to better propagate uncertainty about ambiguous inputs.