Similarity metrics are a core component of many information retrieval and machine learning systems. In this work we propose a method capable of learning a similarity metric from data equipped with a binary relation. By considering only the similarity constraints, and initially ignoring the features, we are able to learn target vectors for each instance using one of several appropriately designed loss functions. A regression model can then be constructed that maps novel feature vectors to the same target vector space, resulting in a feature extractor that computes vectors for which a predefined metric is a meaningful measure of similarity. We present results on both multiclass and multi-label classification datasets that demonstrate considerably faster convergence, as well as higher accuracy on the majority of the intrinsic evaluation tasks and all extrinsic evaluation tasks.
There is also an extension of NCA to nonlinear transformations of the input data @cite_16 . This method can be viewed as a probabilistic variant of Siamese networks. The nonlinear transformation models used in the original exposition of this method were stacked Restricted Boltzmann Machines, initialised using unsupervised pretraining and subsequently fine-tuned using the NCA loss function.
@cite_16
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Deep learning has been successfully applied to perform non-linear embedding. In this paper, we present supervised embedding techniques that use a deep network to collapse classes. The network is pre-trained using a stack of RBMs, and finetuned using approaches that try to collapse classes. The finetuning is inspired by ideas from NCA, but it uses a Student t-distribution to model the similarities of data points belonging to the same class in the embedding. We investigate two types of objective functions: deep t-distributed MCML (dt-MCML) and deep t-distributed NCA (dt-NCA). Our experiments on two handwritten digit data sets reveal the strong performance of dt-MCML in supervised parametric data visualization, whereas dt-NCA outperforms alternative techniques when embeddings with more than two or three dimensions are constructed, e.g., to obtain good classification performances. Overall, our results demonstrate the advantage of using a deep architecture and a heavy-tailed t-distribution for measuring pairwise similarities in supervised embedding. Abstract Deep neural networks with several layers have recently become a highly successful and popular research topic in machine learning due to their excellent performance in many benchmark problems and applications. A key idea in deep learning is to learn not only the nonlinear mapping between the inputs and outputs but also the underlying structure of the data (input) vectors. In this chapter, we first consider problems with training deep networks using backpropagation-type algorithms. After this, we consider various structures used in deep learning, including restricted Boltzmann machines, deep belief networks, deep Boltzmann machines, and nonlinear autoencoders. In the latter part of this chapter, we discuss in more detail the recently developed neural autoregressive distribution estimator and its variants. We describe an image compression method, consisting of a nonlinear analysis transformation, a uniform quantizer, and a nonlinear synthesis transformation. The transforms are constructed in three successive stages of convolutional linear filters and nonlinear activation functions. Unlike most convolutional neural networks, the joint nonlinearity is chosen to implement a form of local gain control, inspired by those used to model biological neurons. Using a variant of stochastic gradient descent, we jointly optimize the entire model for rate-distortion performance over a database of training images, introducing a continuous proxy for the discontinuous loss function arising from the quantizer. Under certain conditions, the relaxed loss function may be interpreted as the log likelihood of a generative model, as implemented by a variational autoencoder. Unlike these models, however, the compression model must operate at any given point along the rate-distortion curve, as specified by a trade-off parameter. Across an independent set of test images, we find that the optimized method generally exhibits better rate-distortion performance than the standard JPEG and JPEG 2000 compression methods. More importantly, we observe a dramatic improvement in visual quality for all images at all bit rates, which is supported by objective quality estimates using MS-SSIM. Some of the main challenges in skeleton-based action recognition systems are redundant and noisy pose transformations. Earlier works in skeleton-based action recognition explored different approaches for filtering linear noise transformations, but neglect to address potential nonlinear transformations. In this paper, we present an unsupervised learning approach for estimating nonlinear noise transformations in pose estimates. Our approach starts by decoupling linear and nonlinear noise transformations. While the linear transformations are modelled explicitly the nonlinear transformations are learned from data. Subsequently, we use an autoencoder with L2-norm reconstruction error and show that it indeed does capture nonlinear noise transformations, and recover a denoised pose estimate which in turn improves performance significantly. We validate our approach on a publicly available dataset, NW-UCLA. Learning based hashing plays a pivotal role in large-scale visual search. However, most existing hashing algorithms tend to learn shallow models that do not seek representative binary codes. In this paper, we propose a novel hashing approach based on unsupervised deep learning to hierarchically transform features into hash codes. Within the heterogeneous deep hashing framework, the autoencoder layers with specific constraints are considered to model the nonlinear mapping between features and binary codes. Then, a Restricted Boltzmann Machine (RBM) layer with constraints is utilized to reduce the dimension in the hamming space. Extensive experiments on the problem of visual search demonstrate the competitiveness of our proposed approach compared to state-of-the-art. We develop a novel modeling framework for Boltzmann machines, augmenting each hidden unit with a latent transformation assignment variable which describes the selection of the transformed view of the canonical connection weights associated with the unit. This enables the inferences of the model to transform in response to transformed input data in a stable and predictable way, and avoids learning multiple features differing only with respect to the set of transformations. Extending prior work on translation equivariant (convolutional) models, we develop translation and rotation equivariant restricted Boltzmann machines (RBMs) and deep belief nets (DBNs), and demonstrate their effectiveness in learning frequently occurring statistical structure from artificial and natural images. Unsupervised learning algorithms aim to discover the structure hidden in the data, and to learn representations that are more suitable as input to a supervised machine than the raw input. Many unsupervised methods are based on reconstructing the input from the representation, while constraining the representation to have certain desirable properties (e.g. low dimension, sparsity, etc). Others are based on approximating density by stochastically reconstructing the input from the representation. We describe a novel and efficient algorithm to learn sparse representations, and compare it theoretically and experimentally with a similar machine trained probabilistically, namely a Restricted Boltzmann Machine. We propose a simple criterion to compare and select different unsupervised machines based on the trade-off between the reconstruction error and the information content of the representation. We demonstrate this method by extracting features from a dataset of handwritten numerals, and from a dataset of natural image patches. We show that by stacking multiple levels of such machines and by training sequentially, high-order dependencies between the input observed variables can be captured. We introduce Deep Canonical Correlation Analysis (DCCA), a method to learn complex nonlinear transformations of two views of data such that the resulting representations are highly linearly correlated. Parameters of both transformations are jointly learned to maximize the (regularized) total correlation. It can be viewed as a nonlinear extension of the linear method canonical correlation analysis (CCA). It is an alternative to the nonparametric method kernel canonical correlation analysis (KCCA) for learning correlated nonlinear transformations. Unlike KCCA, DCCA does not require an inner product, and has the advantages of a parametric method: training time scales well with data size and the training data need not be referenced when computing the representations of unseen instances. In experiments on two real-world datasets, we find that DCCA learns representations with significantly higher correlation than those learned by CCA and KCCA. We also introduce a novel non-saturating sigmoid function based on the cube root that may be useful more generally in feedforward neural networks. Learning invariant representations is an important problem in machine learning and pattern recognition. In this paper, we present a novel framework of transformation-invariant feature learning by incorporating linear transformations into the feature learning algorithms. For example, we present the transformation-invariant restricted Boltzmann machine that compactly represents data by its weights and their transformations, which achieves invariance of the feature representation via probabilistic max pooling. In addition, we show that our transformation-invariant feature learning framework can also be extended to other unsupervised learning methods, such as autoencoders or sparse coding. We evaluate our method on several image classification benchmark datasets, such as MNIST variations, CIFAR-10, and STL-10, and show competitive or superior classification performance when compared to the state-of-the-art. Furthermore, our method achieves state-of-the-art performance on phone classification tasks with the TIMIT dataset, which demonstrates wide applicability of our proposed algorithms to other domains. This paper presents a novel semi-supervised learning algorithm called Active Deep Networks (ADN), to address the semi-supervised sentiment classification problem with active learning. First, we propose the semi-supervised learning method of ADN. ADN is constructed by Restricted Boltzmann Machines (RBM) with unsupervised learning using labeled data and abundant of unlabeled data. Then the constructed structure is fine-tuned by gradient-descent based supervised learning with an exponential loss function. Second, we apply active learning in the semi-supervised learning framework to identify reviews that should be labeled as training data. Then ADN architecture is trained by the selected labeled data and all unlabeled data. Experiments on five sentiment classification datasets show that ADN outperforms the semi-supervised learning algorithm and deep learning techniques applied for sentiment classification. This work presents a general unsupervised learning method to improve the accuracy of sequence to sequence (seq2seq) models. In our method, the weights of the encoder and decoder of a seq2seq model are initialized with the pretrained weights of two language models and then fine-tuned with labeled data. We apply this method to challenging benchmarks in machine translation and abstractive summarization and find that it significantly improves the subsequent supervised models. Our main result is that the pretraining accelerates training and improves generalization of seq2seq models, achieving state-of-the-art results on the WMT English->German task, surpassing a range of methods using both phrase-based machine translation and neural machine translation. Our method achieves an improvement of 1.3 BLEU from the previous best models on both WMT'14 and WMT'15 English->German. On summarization, our method beats the supervised learning baseline. 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. The superiority of deeply learned pedestrian representations has been reported in very recent literature of person re-identification (re-ID). In this article, we consider the more pragmatic issue of learning a deep feature with no or only a few labels. We propose a progressive unsupervised learning (PUL) method to transfer pretrained deep representations to unseen domains. Our method is easy to implement and can be viewed as an effective baseline for unsupervised re-ID feature learning. Specifically, PUL iterates between (1) pedestrian clustering and (2) fine-tuning of the convolutional neural network (CNN) to improve the initialization model trained on the irrelevant labeled dataset. Since the clustering results can be very noisy, we add a selection operation between the clustering and fine-tuning. At the beginning, when the model is weak, CNN is fine-tuned on a small amount of reliable examples that locate near to cluster centroids in the feature space. As the model becomes stronger, in subsequent iterations, more images are being adaptively selected as CNN training samples. Progressively, pedestrian clustering and the CNN model are improved simultaneously until algorithm convergence. This process is naturally formulated as self-paced learning. We then point out promising directions that may lead to further improvement. Extensive experiments on three large-scale re-ID datasets demonstrate that PUL outputs discriminative features that improve the re-ID accuracy. Our code has been released at https: github.com hehefan Unsupervised-Person-Re-identification-Clustering-and-Fine-tuning. We previously have applied deep autoencoder (DAE) for noise reduction and speech enhancement. However, the DAE was trained using only clean speech. In this study, we further introduce an explicit denoising process in learning the DAE. In training the DAE, we still adopt greedy layer-wised pretraining plus fine tuning strategy. In pretraining, each layer is trained as a one hidden layer neural autoencoder (AE) using noisy-clean speech pairs as input and output (or transformed noisy-clean speech pairs by preceding AEs). Fine tuning was done by stacking all AEs with pretrained parameters for initialization. The trained DAE is used as a filter for speech estimation when noisy speech is given. Speech enhancement experiments were done to examine the performance of the trained denoising DAE. Noise reduction, speech distortion, and perceptual evaluation of speech quality (PESQ) criteria are used in the performance evaluations. Experimental results show that adding depth of the DAE consistently increase the performance when a large training data set is given. In addition, compared with a minimum mean square error based speech enhancement algorithm, our proposed denoising DAE provided superior performance on the three objective evaluations. This work presents a general unsupervised learning method to improve the accuracy of sequence to sequence (seq2seq) models. In our method, the weights of the encoder and decoder of a seq2seq model are initialized with the pretrained weights of two language models and then fine-tuned with labeled data. We apply this method to challenging benchmarks in machine translation and abstractive summarization and find that it significantly improves the subsequent supervised models. Our main result is that pretraining improves the generalization of seq2seq models. We achieve state-of-the art results on the WMT English @math German task, surpassing a range of methods using both phrase-based machine translation and neural machine translation. Our method achieves a significant improvement of 1.3 BLEU from the previous best models on both WMT'14 and WMT'15 English @math German. We also conduct human evaluations on abstractive summarization and find that our method outperforms a purely supervised learning baseline in a statistically significant manner. Deep learning subsumes algorithms that automatically learn compositional representations. The ability of these models to generalize well has ushered in tremendous advances in many fields. We propose that software engineering (SE) research is a unique opportunity to use these transformative approaches. Our research examines applications of deep architectures such as recurrent neural networks and stacked restricted Boltzmann machines to SE tasks. Neighborhood Components Analysis (NCA) is a popular method for learning a distance metric to be used within a k-nearest neighbors (kNN) classifier. A key assumption built into the model is that each point stochastically selects a single neighbor, which makes the model well-justified only for kNN with k = 1. However, kNN classifiers with k > 1 are more robust and usually preferred in practice. Here we present kNCA, which generalizes NCA by learning distance metrics that are appropriate for kNN with arbitrary k. The main technical contribution is showing how to efficiently compute and optimize the expected accuracy of a kNN classifier. We apply similar ideas in an unsupervised setting to yield kSNE and kt-SNE, generalizations of Stochastic Neighbor Embedding (SNE, t-SNE) that operate on neighborhoods of size k, which provide an axis of control over embeddings that allow for more homogeneous and interpretable regions. Empirically, we show that kNCA often improves classification accuracy over state of the art methods, produces qualitative differences in the embeddings as k is varied, and is more robust with respect to label noise. Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep learning by systematically analyzing learning dynamics for the restricted case of deep linear neural networks. Despite the linearity of their input-output map, such networks have nonlinear gradient descent dynamics on weights that change with the addition of each new hidden layer. We show that deep linear networks exhibit nonlinear learning phenomena similar to those seen in simulations of nonlinear networks, including long plateaus followed by rapid transitions to lower error solutions, and faster convergence from greedy unsupervised pretraining initial conditions than from random initial conditions. We provide an analytical description of these phenomena by finding new exact solutions to the nonlinear dynamics of deep learning. Our theoretical analysis also reveals the surprising finding that as the depth of a network approaches infinity, learning speed can nevertheless remain finite: for a special class of initial conditions on the weights, very deep networks incur only a finite, depth independent, delay in learning speed relative to shallow networks. We show that, under certain conditions on the training data, unsupervised pretraining can find this special class of initial conditions, while scaled random Gaussian initializations cannot. We further exhibit a new class of random orthogonal initial conditions on weights that, like unsupervised pre-training, enjoys depth independent learning times. We further show that these initial conditions also lead to faithful propagation of gradients even in deep nonlinear networks, as long as they operate in a special regime known as the edge of chaos. Videos always exhibit various pattern motions, which can be modeled according to dynamics between adjacent frames. Previous methods based on linear dynamic system can model dynamic textures but have limited capacity of representing sophisticated nonlinear dynamics. Inspired by the nonlinear expression power of deep autoencoders, we propose a novel model named dynencoder which has an autoencoder at the bottom and a variant of it at the top (named as dynpredictor). It generates hidden states from raw pixel inputs via the autoencoder and then encodes the dynamic of state transition over time via the dynpredictor. Deep dynencoder can be constructed by proper stacking strategy and trained by layer-wise pre-training and joint fine-tuning. Experiments verify that our model can describe sophisticated video dynamics and synthesize endless video texture sequences with high visual quality. We also design classification and clustering methods based on our model and demonstrate the efficacy of them on traffic scene classification and motion segmentation. To allow the hidden units of a restricted Boltzmann machine to model the transformation between two successive images, Memisevic and Hinton (2007) introduced three-way multiplicative interactions that use the intensity of a pixel in the first image as a multiplicative gain on a learned, symmetric weight between a pixel in the second image and a hidden unit. This creates cubically many parameters, which form a three-dimensional interaction tensor. We describe a low-rank approximation to this interaction tensor that uses a sum of factors, each of which is a three-way outer product. This approximation allows efficient learning of transformations between larger image patches. Since each factor can be viewed as an image filter, the model as a whole learns optimal filter pairs for efficiently representing transformations. We demonstrate the learning of optimal filter pairs from various synthetic and real image sequences. We also show how learning about image transformations allows the model to perform a simple visual analogy task, and we show how a completely unsupervised network trained on transformations perceives multiple motions of transparent dot patterns in the same way as humans.