Multimodal learning with deep Boltzmann machines (DBMs) is an generative approach to fuse multimodal inputs, and can learn the shared representation via Contrastive Divergence (CD) for classification and information retrieval tasks. However, it is a 2-fan DBM model, and cannot effectively handle multiple prediction tasks. Moreover, this model cannot recover the hidden representations well by sampling from the conditional distribution when more than one modalities are missing. In this paper, we propose a K-fan deep structure model, which can handle the multi-input and muti-output learning problems effectively. In particular, the deep structure has K-branch for different inputs where each branch can be composed of a multi-layer deep model, and a shared representation is learned in an discriminative manner to tackle multimodal tasks. Given the deep structure, we propose two objective functions to handle two multi-input and multi-output tasks: joint visual restoration and labeling, and the multi-view multi-calss object recognition tasks. To estimate the model parameters, we initialize the deep model parameters with CD to maximize the joint distribution, and then we use backpropagation to update the model according to specific objective function. The experimental results demonstrate that the model can effectively leverages multi-source information and predict multiple tasks well over competitive baselines.

In this paper, we provide a new neural-network based perspective on multi-task learning (MTL) and multi-domain learning (MDL). By introducing the concept of a semantic descriptor, this framework unifies MDL and MTL as well as encompassing various classic and recent MTL/MDL algorithms by interpreting them as different ways of constructing semantic descriptors. Our interpretation provides an alternative pipeline for zero-shot learning (ZSL), where a model for a novel class can be constructed without training data. Moreover, it leads to a new and practically relevant problem setting of zero-shot domain adaptation (ZSDA), which is the analogous to ZSL but for novel domains: A model for an unseen domain can be generated by its semantic descriptor. Experiments across this range of problems demonstrate that our framework outperforms a variety of alternatives.

Abstract--This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., We generalize AST (atomic-norm soft thresholding) to the case of nonconsecutively sampled data (incomplete data) inspired by recent atomic norm based techniques. We present a gridless version of SPICE (gridless SPICE, or GLS), which is applicable to both complete and incomplete data without the knowledge of noise level. We further prove the equivalence between GLS and atomic norm-based techniques under different assumptions of noise. Moreover, we extend GLS to a systematic framework consisting of model order selection and robust frequency estimation, and present feasible algorithms for AST and GLS. Numerical simulations are provided to validate our theoretical analysis and demonstrate performance of our methods compared to existing ones. Spectral analysis of signals [1] is a major problem in statistical signal processing. In this paper we are concerned about the line spectral estimation problem which has wide applications in communications, radar, sonar, seismology, astronomy and so on. C is the measurement noise. The sinusoid numberK M, usually referred to as the model order, is typically unknown in practice. Following from [2], the case when the signal is observed on [M ] is referred to as the complete data case while the other case when only samples on Ω [M ] are available is called the incomplete data case (or missing data case), in which the samples on the complementary set of Ω, Ω, [M ]\ Ω, are called missing data. Manuscript November 2013; accepted by IEEE Transactions on Signal Processing March 2015. The authors are with the School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore (email: { yangzai, elhxie } @ntu.edu.sg). Frequency estimation and model order selection are two important topics in line spectral estimation. 's can be obtained by a simple least-squares method according to (1). This paper is mainly focused on frequency estimation but we also incorporate existing model order selection tools in our methods. Many methods have been proposed for frequency estimation. Common classical methods include periodogram (or beamforming), nonlinear least squares (NLS) and MUSIC but often have limitations (see the review in [1]). For example, the periodogram suffers from leakage problems and have difficulties in resolving closely separated frequencies [1]. It is worth noting that the recent iterative adaptive approach (IAA) [4], [5] reduces the leakage of periodogram.

We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper constraints on the matrix $M$, and establish theoretical upper and lower bounds on the recovery error. Our bounds are nearly optimal up to a factor on the order of $\mathcal{O}(\log(d_1 d_2))$. These bounds are obtained by adapting the arguments used for one-bit matrix completion \cite{davenport20121} (although these two problems are different in nature) and the adaptation requires new techniques exploiting properties of the Poisson likelihood function and tackling the difficulties posed by the locally sub-Gaussian characteristic of the Poisson distribution. Our results highlight a few important distinctions of Poisson matrix completion compared to the prior work in matrix completion including having to impose a minimum signal-to-noise requirement on each observed entry. We also develop an efficient iterative algorithm and demonstrate its good performance in recovering solar flare images.

Neuroimage analysis usually involves learning thousands or even millions of variables using only a limited number of samples. In this regard, sparse models, e.g. the lasso, are applied to select the optimal features and achieve high diagnosis accuracy. The lasso, however, usually results in independent unstable features. Stability, a manifest of reproducibility of statistical results subject to reasonable perturbations to data and the model (Yu 2013), is an important focus in statistics, especially in the analysis of high dimensional data. In this paper, we explore a nonnegative generalized fused lasso model for stable feature selection in the diagnosis of Alzheimer's disease. In addition to sparsity, our model incorporates two important pathological priors: the spatial cohesion of lesion voxels and the positive correlation between the features and the disease labels. To optimize the model, we propose an efficient algorithm by proving a novel link between total variation and fast network flow algorithms via conic duality. Experiments show that the proposed nonnegative model performs much better in exploring the intrinsic structure of data via selecting stable features compared with other state-of-the-arts.

Linear classifiers play a central role in supervised learning, with a rich and elegant theory. This setting assumes data is represented as points in a Hilbert space, either explicitly as feature vectors or implicitly via a kernel. A significant strength of the Hilbert-space model is its inner-product structure, which has been exploited statistically and algorithmically by sophisticated techniques from geometric and functional analysis, placing the celebrated hyperplane methods on a solid foundation. However, the success of the Hilbert-space model obscures its limitations -- perhaps the most significant of which is that it cannot represent many norms and distance functions that arise naturally in applications.

Measuring the morphological parameters of galaxies is a key requirement for studying their formation and evolution. Surveys such as the Sloan Digital Sky Survey (SDSS) have resulted in the availability of very large collections of images, which have permitted population-wide analyses of galaxy morphology. Morphological analysis has traditionally been carried out mostly via visual inspection by trained experts, which is time-consuming and does not scale to large ($\gtrsim10^4$) numbers of images. Although attempts have been made to build automated classification systems, these have not been able to achieve the desired level of accuracy. The Galaxy Zoo project successfully applied a crowdsourcing strategy, inviting online users to classify images by answering a series of questions. Unfortunately, even this approach does not scale well enough to keep up with the increasing availability of galaxy images. We present a deep neural network model for galaxy morphology classification which exploits translational and rotational symmetry. It was developed in the context of the Galaxy Challenge, an international competition to build the best model for morphology classification based on annotated images from the Galaxy Zoo project. For images with high agreement among the Galaxy Zoo participants, our model is able to reproduce their consensus with near-perfect accuracy ($> 99\%$) for most questions. Confident model predictions are highly accurate, which makes the model suitable for filtering large collections of images and forwarding challenging images to experts for manual annotation. This approach greatly reduces the experts' workload without affecting accuracy. The application of these algorithms to larger sets of training data will be critical for analysing results from future surveys such as the LSST.

This paper considers a multiple regression model and compares, under full model hypothesis, analytically as well as by simulation, the performance characteristics of some popular penalty estimators such as ridge regression, LASSO, adaptive LASSO, SCAD, and elastic net versus Least Squares Estimator, restricted estimator, preliminary test estimator, and Stein-type estimators when the dimension of the parameter space is smaller than the sample space dimension. We find that RR uniformly dominates LSE, RE, PTE, SE and PRSE while LASSO, aLASSO, SCAD, and EN uniformly dominates LSE only. Further, it is observed that neither penalty estimators nor Stein-type estimator dominate one another.

There is a rapidly increasing interest in crowdsourcing for data labeling. By crowdsourcing, a large number of labels can be often quickly gathered at low cost. However, the labels provided by the crowdsourcing workers are usually not of high quality. In this paper, we propose a minimax conditional entropy principle to infer ground truth from noisy crowdsourced labels. Under this principle, we derive a unique probabilistic labeling model jointly parameterized by worker ability and item difficulty. We also propose an objective measurement principle, and show that our method is the only method which satisfies this objective measurement principle. We validate our method through a variety of real crowdsourcing datasets with binary, multiclass or ordinal labels.

We establish upper bounds for the minimal number of hidden units for which a binary stochastic feedforward network with sigmoid activation probabilities and a single hidden layer is a universal approximator of Markov kernels. We show that each possible probabilistic assignment of the states of $n$ output units, given the states of $k\geq1$ input units, can be approximated arbitrarily well by a network with $2^{k-1}(2^{n-1}-1)$ hidden units.