Knowledge of biological processes captured in such equations, when solutions to them match measurements made from the system of interest, help confirm our understanding of systems level function. Examples of such models include cell cycle progression (Chen et al., 2000), integrate and fire generation of heart pacemaker pulses (Zhang et al., 2000) and cellular behavior in synchrony with the circadian cycle (Leloup and Goldbeter, 2003). A particular appeal of modeling is that models can be interrogated with what if type questions to improve our understanding of the system, or be used to make quantitative predictions in domains in which measurements are unavailable. A central issue in developing computational models of biological systems is setting parameters such as rate constants of biochemical reactions, synthesis and decay rates of macromolecules, delays incurred in transcription of genes and translation of proteins, and sharpness of nonlinear effects (Hill coefficient) are examples of such parameters. Parameter values are usually determined by conducting in vitro experiments (e.g.

To be published as a chapter in'Adaptive Learning Methods for Nonlinear System Modeling', Elsevier Publishing, Eds. Abstract In this chapter, we analyze nonlinear filtering problems in distributed environments, e.g., sensor networks or peer-to-peer protocols. In these scenarios, the agents in the environment receive measurements in a streaming fashion, and they are required to estimate a common (nonlinear) model by alternating local computations and communications with their neighbors. We focus on the important distinction between single-task problems, where the underlying model is common to all agents, and multitask problems, where each agent might converge to a different model due to, e.g., spatial dependencies or other factors. Currently, most of the literature on distributed learning in the nonlinear case has focused on the single-task case, which may be a strong limitation in real-world scenarios. After introducing the problem and reviewing the existing approaches, we describe a simple kernel-based algorithm tailored for the multitask case. We evaluate the proposal on a simulated benchmark task, and we conclude by detailing currently open problems and lines of research.

Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implicitly in different works in the literature. The provided analysis yields several theoretical and practical consequences. For instance, we discuss the application of GIS into the Sequential Importance Resampling framework and show that Independent Multiple Try Metropolis schemes can be interpreted as a standard Metropolis-Hastings algorithm, following the GIS approach. We also introduce two novel Markov Chain Monte Carlo (MCMC) techniques based on GIS. The first one, named Group Metropolis Sampling method, produces a Markov chain of sets of weighted samples. All these sets are then employed for obtaining a unique global estimator. The second one is the Distributed Particle Metropolis-Hastings technique, where different parallel particle filters are jointly used to drive an MCMC algorithm. Different resampled trajectories are compared and then tested with a proper acceptance probability. The novel schemes are tested in different numerical experiments such as learning the hyperparameters of Gaussian Processes, the localization problem in a wireless sensor network and the tracking of vegetation parameters given satellite observations, where they are compared with several benchmark Monte Carlo techniques. Three illustrative Matlab demos are also provided.

Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired maximum entropy distribution. Doing so is nontrivial in that the objective being maximized (entropy) is a function of the density itself. By exploiting recent developments in normalizing flow networks, we cast the maximum entropy problem into a finite-dimensional constrained optimization, and solve the problem by combining stochastic optimization with the augmented Lagrangian method. Simulation results demonstrate the effectiveness of our method, and applications to finance and computer vision show the flexibility and accuracy of using maximum entropy flow networks.

Muti-dimensional datasets are now prevalent across the sciences; their ubiquity and importance will only continue to grow [1-4]. The analysis of data demands methods that preserve multidimensional structures, and that exploit them. We introduce a versatile data clustering framework based on tensors (high dimensional arrays) and algebra to analyze multidimensional datasets. One key feature of this method is that it can incorporate general, application-specific constraints on the composition of a cluster, and is guaranteed to find optimal partitions. The flexibility of the method allows it to be used directly on a dataset (i.e., as a standalone clustering tool), or in combination with other clustering methods. We apply our method on an extensive set of timecourse measurements of the activation levels of the mitogen-activated protein kinase (MAPK) and phosphoinositide 3-kinase (PI3K) pathways that are involved in cellular decisions and fates [10-13], and are known to dysfunction in cancer [10-13, 16]. The key signaling proteins and subtype responses in breast cancer cells are known; however, among genetically diverse cell lines the dysfunction varies and is not well understood [1, 15, 16]. Our objective is to find groups of cell lines whose signal transduction networks have similar dynamics. A high similarity suggests that the cell lines share pathway features that can be relevant for the responses to the ligands.

This formula-free summary provides a short overview about how PCA (principal component analysis) works for dimension reduction, that is, to select k features (also called variables) among a larger set of n features, with k much smaller than n. This smaller set of k features built with PCA is the best subset of k features, in the sense that it minimizes the variance of the residual noise when fitting data to a linear model. Note that PCA transforms the initial features into new ones, that are linear combinations of the original features.

Good profitable customers rarely become unprofitable. It is more likely that they were unprofitable from the onset. Determining an approach to define customer value can be a complex decision. Traditionally, we use gross margin in identifying good and bad customers. For example, if your overhead costs are 25% of gross revenue, a good customer is anyone with a gross margin over 25%.

Machine learning is one of the hottest new technologies to emerge into popular consciousness in the last decade, transforming fields from consumer electronics and healthcare to retail. This has led to intense curiosity about this field among many students and working professionals about the field. If you're a tech professional such as a software developer, business analyst or even a product manager, you might be curious about how machine learning can change they way you work and take your career to the next level. However, as a busy professional, you're also looking for a way to get a solid understanding of machine learning that's not only rigorous and practical, but also concise and fast. This machine learning tutorial will help you achieve your goals.

Integrated Computational Materials Engineering (ICME) aims to accelerate optimal design of complex material systems by integrating material science and design automation. For tractable ICME, it is required that (1) a structural feature space be identified to allow reconstruction of new designs, and (2) the reconstruction process be property-preserving. The majority of existing structural presentation schemes rely on the designer's understanding of specific material systems to identify geometric and statistical features, which could be biased and insufficient for reconstructing physically meaningful microstructures of complex material systems. In this paper, we develop a feature learning mechanism based on convolutional deep belief network to automate a two-way conversion between microstructures and their lower-dimensional feature representations, and to achieves a 1000-fold dimension reduction from the microstructure space. The proposed model is applied to a wide spectrum of heterogeneous material systems with distinct microstructural features including Ti-6Al-4V alloy, Pb63-Sn37 alloy, Fontainebleau sandstone, and Spherical colloids, to produce material reconstructions that are close to the original samples with respect to 2-point correlation functions and mean critical fracture strength. This capability is not achieved by existing synthesis methods that rely on the Markovian assumption of material microstructures.

This paper addresses the problem of handling spatial misalignments due to camera-view changes or human-pose variations in person re-identification. We first introduce a boosting-based approach to learn a correspondence structure which indicates the patch-wise matching probabilities between images from a target camera pair. The learned correspondence structure can not only capture the spatial correspondence pattern between cameras but also handle the viewpoint or human-pose variation in individual images. We further introduce a global constraint-based matching process. It integrates a global matching constraint over the learned correspondence structure to exclude cross-view misalignments during the image patch matching process, hence achieving a more reliable matching score between images. Finally, we also extend our approach by introducing a multi-structure scheme, which learns a set of local correspondence structures to capture the spatial correspondence sub-patterns between a camera pair, so as to handle the spatial misalignments between individual images in a more precise way. Experimental results on various datasets demonstrate the effectiveness of our approach.