We consider the problem of learning a coefficient vector x0 from noisy linear observation y=Ax0+w. In many contexts (ranging from model selection to image processing) it is desirable to construct a sparse estimator. In this case, a popular approach consists in solving an l1-penalized least squares problem known as the LASSO or BPDN. For sequences of matrices A of increasing dimensions, with iid gaussian entries, we prove that the normalized risk of the LASSO converges to a limit, and we obtain an explicit expression for this limit. Our result is the first rigorous derivation of an explicit formula for the asymptotic risk of the LASSO for random instances. The proof technique is based on the analysis of AMP, a recently developed efficient algorithm, that is inspired from graphical models ideas. Through simulations on real data matrices (gene expression data and hospital medical records) we observe that these results can be relevant in a broad array of practical applications.

To understand the relationship between genomic variations among population and complex diseases, it is essential to detect eQTLs which are associated with phenotypic effects.However, detecting eQTLs remains a challenge due to complex underlying mechanisms and the very large number of genetic loci involved compared tothe number of samples. Thus, to address the problem, it is desirable to take advantage of the structure of the data and prior information about genomic locations such as conservation scores and transcription factor binding sites. In this paper, we propose a novel regularized regression approach for detecting eQTLs which takes into account related traits simultaneously while incorporating many regulatory features. We first present a Bayesian network for a multi-task learning problem that includes priors on SNPs, making it possible to estimate the significance of each covariate adaptively. Then we find the maximum a posteriori (MAP) estimation of regression coefficients and estimate weights of covariates jointly. This optimization procedure is efficient since it can be achieved by using aprojected gradient descent and a coordinate descent procedure iteratively. Experimental results on simulated and real yeast datasets confirm that our model outperforms previous methods for finding eQTLs.

In multi-instance learning, there are two kinds of prediction failure, i.e., false negative and false positive. Current research mainly focus on avoding the former. We attempt to utilize the geometric distribution of instances inside positive bags to avoid both the former and the latter. Based on kernel principal component analysis, we define a projection constraint for each positive bag to classify its constituent instances far away from the separating hyperplane while place positive instances and negative instances at opposite sides. We apply the Constrained Concave-Convex Procedure to solve the resulted problem. Empirical results demonstrate that our approach offers improved generalization performance.

The problem of optimal and automatic design of a detector cascade is considered. A novel mathematical model is introduced for a cascaded detector. This model is analytically tractable, leads to recursive computation, and accounts for both classification and complexity. A boosting algorithm, FCBoost, is proposed for fully automated cascade design. It exploits the new cascade model, minimizes a Lagrangian cost that accounts for both classification risk and complexity. It searches the space of cascade configurations to automatically determine the optimal number of stages and their predictors, and is compatible with bootstrapping of negative examples and cost sensitive learning. Experiments show that the resulting cascades have state-of-the-art performance in various computer vision problems.

Activity of a neuron, even in the early sensory areas, is not simply a function of its local receptive field or tuning properties, but depends on global context of the stimulus, as well as the neural context. This suggests the activity of the surrounding neurons and global brain states can exert considerable influence on the activity of a neuron. In this paper we implemented an L1 regularized point process model to assess the contribution of multiple factors to the firing rate of many individual units recorded simultaneously from V1 with a 96-electrode "Utah" array. We found that the spikes of surrounding neurons indeed provide strong predictions of a neuron's response, in addition to the neuron's receptive field transfer function. We also found that the same spikes could be accounted for with the local field potentials, a surrogate measure of global network states. This work shows that accounting for network fluctuations can improve estimates of single trial firing rate and stimulus-response transfer functions.

Regularization technique has become a principle tool for statistics and machine learning research and practice. However, in most situations, these regularization terms are not well interpreted, especially on how they are related to the loss function and data. In this paper, we propose a robust minimax framework to interpret the relationship between data and regularization terms for a large class of loss functions. We show that various regularization terms are essentially corresponding to different distortions to the original data matrix. This minimax framework includes ridge regression, lasso, elastic net, fused lasso, group lasso, local coordinate coding, multiple kernel learning, etc., as special cases. Within this minimax framework, we further gave mathematically exact definition for a novel representation called sparse grouping representation (SGR), and proved sufficient conditions for generating such group level sparsity. Under these sufficient conditions, a large set of consistent regularization terms can be designed. This SGR is essentially different from group lasso in the way of using class or group information, and it outperforms group lasso when there appears group label noise. We also gave out some generalization bounds in a classification setting.

Network models are widely used to capture interactions among component of complex systems, such as social and biological. To understand their behavior, it is often necessary to analyze functionally related components of the system, corresponding to subsystems. Therefore, the analysis of subnetworks may provide additional insight into the behavior of the system, not evident from individual components. We propose a novel approach for incorporating available network information into the analysis of arbitrary subnetworks. The proposed method offers an efficient dimension reduction strategy using Laplacian eigenmaps with Neumann boundary conditions, and provides a flexible inference framework for analysis of subnetworks, based on a group-penalized principal component regression model on graphs. Asymptotic properties of the proposed inference method, as well as the choice of the tuning parameter for control of the false positive rate are discussed in high dimensional settings. The performance of the proposed methodology is illustrated using simulated and real data examples from biology.

We address the problem of estimating the F-measure of a given model as accurately as possible on a fixed labeling budget. This problem occurs whenever an estimate cannot be obtained from held-out training data; for instance, when data that have been used to train the model are held back for reasons of privacy or do not reflect the test distribution. In this case, new test instances have to be drawn and labeled at a cost. An active estimation procedure selects instances according to an instrumental sampling distribution. An analysis of the sources of estimation error leads to an optimal sampling distribution that minimizes estimator variance. We explore conditions under which active estimates of F-measures are more accurate than estimates based on instances sampled from the test distribution.

Several motor related Brain Computer Interfaces (BCIs) have been developed over the years that use activity decoded from the contralateral hemisphere to operate devices. Contralateralprimary motor cortex is also the region most severely affected by hemispheric stroke. Recent studies have identified ipsilateral cortical activity in planning of motor movements and its potential implications for a stroke relevant BCI.The most fundamental functional loss after a hemispheric stroke is the loss of fine motor control of the hand. Thus, whether ipsilateral cortex encodes finger movements is critical to the potential feasibility of BCI approaches in the future. This study uses ipsilateral cortical signals from humans (using ECoG) to decode finger movements. We demonstrate, for the first time, successful finger movement detection using machine learning algorithms. Our results show high decoding accuracies in all cases which are always above chance. We also show that significant accuracies can be achieved with the use of only a fraction of all the features recorded and that these core features are consistent with previous physiological findings.The results of this study have substantial implications for advancing neuroprosthetic approaches to stroke populations not currently amenable to existing BCI techniques.

Multiple-Instance learning has been long known as a hard non-convex problem. In this work, we propose an approach that recasts it as a convex likelihood ratio estimation problem. Firstly, the constraint in multiple-instance learning is reformulated into a convex constraint on the likelihood ratio. Then we show that a joint estimation of a likelihood ratio function and the likelihood on training instances can be learned convexly. Theoretically, we prove a quantitative relationship between the risk estimated under the 0-1 classification loss, and under a loss function for likelihood ratio estimation. It is shown that our likelihood ratio estimation is generally a good surrogate for the 0-1 loss, and separates positive and negative instances well. However with the joint estimation it tends to underestimate the likelihood of an example to be positive. We propose to use these likelihood ratio estimates as features, and learn a linear combination on them to classify the bags. Experiments on synthetic and real datasets show the superiority of the approach.