Incorporating invariances into a learning algorithm is a common problem in machine learning. We provide a convex formulation which can deal with arbitrary loss functions and arbitrary losses. In addition, it is a drop-in replacement for most optimization algorithms for kernels, including solvers of the SVMStruct family. The advantage of our setting is that it relies on column generation instead of modifying the underlying optimization problem directly.

Maximum entropy analysis of binary variables provides an elegant way for studying the role of pairwise correlations in neural populations. Unfortunately, these approaches suffer from their poor scalability to high dimensions. In sensory coding, however, high-dimensional data is ubiquitous. Here, we introduce a new approach using a near-maximum entropy model, that makes this type of analysis feasible for very high-dimensional data--the model parameters can be derived in closed form and sampling is easy. Therefore, our NearMaxEnt approach can serve as a tool for testing predictions from a pairwise maximum entropy model not only for low-dimensional marginals, but also for high dimensional measurements of more than thousand units. We demonstrate its usefulness by studying natural images with dichotomized pixel intensities. Our results indicate that the statistics of such higher-dimensional measurements exhibit additional structure that are not predicted by pairwise correlations, despite the fact that pairwise correlations explain the lower-dimensional marginal statistics surprisingly well up to the limit of dimensionality where estimation of the full joint distribution is feasible.

There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models, especially in connection with difficulties in computing maximum likelihood estimates. The issues associated with these difficulties relate to the broader structure of discrete exponential families. This paper re-examines the issues in two parts. First we consider the closure of $k$-dimensional exponential families of distribution with discrete base measure and polyhedral convex support $\mathrm{P}$. We show that the normal fan of $\mathrm{P}$ is a geometric object that plays a fundamental role in deriving the statistical and geometric properties of the corresponding extended exponential families. We discuss its relevance to maximum likelihood estimation, both from a theoretical and computational standpoint. Second, we apply our results to the analysis of ERG models. In particular, by means of a detailed example, we provide some characterization of the properties of ERG models, and, in particular, of certain behaviors of ERG models known as degeneracy.

We have proposed a model based upon flocking on a complex network, and then developed two clustering algorithms on the basis of it. In the algorithms, firstly a \textit{k}-nearest neighbor (knn) graph as a weighted and directed graph is produced among all data points in a dataset each of which is regarded as an agent who can move in space, and then a time-varying complex network is created by adding long-range links for each data point. Furthermore, each data point is not only acted by its \textit{k} nearest neighbors but also \textit{r} long-range neighbors through fields established in space by them together, so it will take a step along the direction of the vector sum of all fields. It is more important that these long-range links provides some hidden information for each data point when it moves and at the same time accelerate its speed converging to a center. As they move in space according to the proposed model, data points that belong to the same class are located at a same position gradually, whereas those that belong to different classes are away from one another. Consequently, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the rates of convergence of clustering algorithms are fast enough. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.

Dimensional reduction of high dimensional data can be achieved by keeping only the relevant eigenmodes after principal component analysis. However, differentiating relevant eigenmodes from the random noise eigenmodes is problematic. A new method based on the random matrix theory and a statistical goodness-of-fit test is proposed in this paper. It is validated by numerical simulations and applied to real-time magnetic resonance cardiac cine images.

Self-organizing networks such as Neural Gas, Growing Neural Gas and many others have been adopted in actual applications for both dimensionality reduction and manifold learning. Typically, in these applications, the structure of the adapted network yields a good estimate of the topology of the unknown subspace from where the input data points are sampled. The approach presented here takes a different perspective, namely by assuming that the input space is a manifold of known dimension. In return, the new type of growing self-organizing network presented gains the ability to adapt itself in way that may guarantee the effective and stable recovery of the exact topological structure of the input manifold.

We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it does not impose any submodularity constraints; instead we require planarity to establish a correspondence with perfect matchings (dimer coverings) in an expanded dual graph. We implement a unified framework while delegating complex but well-understood subproblems (planar embedding, maximum-weight perfect matching) to established algorithms for which efficient implementations are freely available. Unlike graph cut methods, we can perform penalized maximum-likelihood as well as maximum-margin parameter estimation in the associated conditional random fields (CRFs), and employ marginal posterior probabilities as well as maximum a posteriori (MAP) states for prediction. Maximum-margin CRF parameter estimation on image denoising and segmentation problems shows our approach to be efficient and effective. A C++ implementation is available from http://nic.schraudolph.org/isinf/

We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The large-sample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where the tuning results in consistent model selection. We show that the finite-sample as well as the large-sample distributions are typically highly non-normal, regardless of the choice of the tuning parameter. The uniform convergence rate is also obtained, and is shown to be slower than $n^{-1/2}$ in case the estimator is tuned to perform consistent model selection. In particular, these results question the statistical relevance of the `oracle' property of the adaptive LASSO estimator established in Zou (2006). Moreover, we also provide an impossibility result regarding the estimation of the distribution function of the adaptive LASSO estimator.The theoretical results, which are obtained for a regression model with orthogonal design, are complemented by a Monte Carlo study using non-orthogonal regressors.

Counting and classifying blood cells is an important diagnostic tool in medicine. Support Vector Machines are increasingly popular and efficient and could replace artificial neural network systems. Here a method to classify blood cells is proposed using SVM. A set of statistics on images are implemented in C++. The MPEG-7 descriptors Scalable Color Descriptor, Color Structure Descriptor, Color Layout Descriptor and Homogeneous Texture Descriptor are extended in size and combined with textural features corresponding to textural properties perceived visually by humans. From a set of images of human blood cells these statistics are collected. A SVM is implemented and trained to classify the cell images. The cell images come from a CellaVision DM-96 machine which classify cells from images from microscopy. The output images and classification of the CellaVision machine is taken as ground truth, a truth that is 90-95% correct. The problem is divided in two -- the primary and the simplified. The primary problem is to classify the same classes as the CellaVision machine. The simplified problem is to differ between the five most common types of white blood cells. An encouraging result is achieved in both cases -- error rates of 10.8% and 3.1% -- considering that the SVM is misled by the errors in ground truth. Conclusion is that further investigation of performance is worthwhile.

Autoencoder neural network is implemented to estimate the missing data. Genetic algorithm is implemented for network optimization and estimating the missing data. Missing data is treated as Missing At Random mechanism by implementing maximum likelihood algorithm. The network performance is determined by calculating the mean square error of the network prediction. The network is further optimized by implementing Decision Forest. The impact of missing data is then investigated and decision forrests are found to improve the results.