Partially Linear Estimation with Application to Sparse Signal Recovery From Measurement Pairs

We address the problem of estimating a random vector X from two sets of measurements Y and Z, such that the estimator is linear in Y. We show that the partially linear minimum mean squared error (PLMMSE) estimator does not require knowing the joint distribution of X and Y in full, but rather only its second-order moments. This renders it of potential interest in various applications. We further show that the PLMMSE method is minimax-optimal among all estimators that solely depend on the second-order statistics of X and Y. We demonstrate our approach in the context of recovering a signal, which is sparse in a unitary dictionary, from noisy observations of it and of a filtered version of it. We show that in this setting PLMMSE estimation has a clear computational advantage, while its performance is comparable to state-of-the-art algorithms. We apply our approach both in static and dynamic estimation applications. In the former category, we treat the problem of image enhancement from blurred/noisy image pairs, where we show that PLMMSE estimation performs only slightly worse than state-of-the art algorithms, while running an order of magnitude faster. In the dynamic setting, we provide a recursive implementation of the estimator and demonstrate its utility in the context of tracking maneuvering targets from position and acceleration measurements.Comment: 13 pages, 5 figure

Deep representation learning: Fundamentals, Perspectives, Applications, and Open Challenges

Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning process. The representations learned in a successful learning process should be concise, discrete, meaningful, and able to be applied across a variety of tasks. A recent effort has been directed toward developing Deep Learning models, which have proven to be particularly effective at capturing high-dimensional, non-linear, and multi-modal characteristics. In this work, we discuss the principles and developments that have been made in the process of learning representations, and converting them into desirable applications. In addition, for each framework or model, the key issues and open challenges, as well as the advantages, are examined

The Neural Tangent Link Between CNN Denoisers and Non-Local Filters

Convolutional Neural Networks (CNNs) are now a well-established tool for solving computational imaging problems. Modern CNN-based algorithms obtain state-of-the-art performance in diverse image restoration problems. Furthermore, it has been recently shown that, despite being highly overparameterized, networks trained with a single corrupted image can still perform as well as fully trained networks. We introduce a formal link between such networks through their neural tangent kernel (NTK), and well-known non-local filtering techniques, such as non-local means or BM3D. The filtering function associated with a given network architecture can be obtained in closed form without need to train the network, being fully characterized by the random initialization of the network weights. While the NTK theory accurately predicts the filter associated with networks trained using standard gradient descent, our analysis shows that it falls short to explain the behaviour of networks trained using the popular Adam optimizer. The latter achieves a larger change of weights in hidden layers, adapting the non-local filtering function during training. We evaluate our findings via extensive image denoising experiments

Distantly-Supervised Named Entity Recognition with Uncertainty-aware Teacher Learning and Student-student Collaborative Learning

Distantly-Supervised Named Entity Recognition (DS-NER) effectively alleviates the burden of annotation, but meanwhile suffers from the label noise. Recent works attempt to adopt the teacher-student framework to gradually refine the training labels and improve the overall robustness. However, we argue that these teacher-student methods achieve limited performance because poor network calibration produces incorrectly pseudo-labeled samples, leading to error propagation. Therefore, we attempt to mitigate this issue by proposing: (1) Uncertainty-aware Teacher Learning that leverages the prediction uncertainty to guide the selection of pseudo-labels, avoiding the number of incorrect pseudo-labels in the self-training stage. (2) Student-student Collaborative Learning that allows the transfer of reliable labels between two student networks instead of completely relying on all pseudo-labels from its teacher. Meanwhile, this approach allows a full exploration of mislabeled samples rather than simply filtering unreliable pseudo-labeled samples. Extensive experimental results on five DS-NER datasets demonstrate that our method is superior to state-of-the-art teacher-student methods

Representation Learning: A Review and New Perspectives

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning