We address the problem of parameter estimation in models of systems biology from noisy observations. The models we consider are characterized by simultaneous deterministic nonlinear differential equations whose parameters are either taken from in vitro experiments, or are hand-tuned during the model development process to reproduces observations from the system. We consider the family of algorithms coming under the Bayesian formulation of Approximate Bayesian Computation (ABC), and show that sensitivity analysis could be deployed to quantify the relative roles of different parameters in the system. Parameters to which a system is relatively less sensitive (known as sloppy parameters) need not be estimated to high precision, while the values of parameters that are more critical (stiff parameters) need to be determined with care. A tradeoff between computational complexity and the accuracy with which the posterior distribution may be probed is an important characteristic of this class of algorithms.

Video analytics requires operating with large amounts of data. Compressive sensing allows to reduce the number of measurements required to represent the video using the prior knowledge of sparsity of the original signal, but it imposes certain conditions on the design matrix. The Bayesian compressive sensing approach relaxes the limitations of the conventional approach using the probabilistic reasoning and allows to include different prior knowledge about the signal structure. This paper presents two Bayesian compressive sensing methods for autonomous object detection in a video sequence from a static camera. Their performance is compared on the real datasets with the non-Bayesian greedy algorithm. It is shown that the Bayesian methods can provide the same accuracy as the greedy algorithm but much faster; or if the computational time is not critical they can provide more accurate results.

One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions and turned out to be a well-known NP-hard problem and, hence, approximations are required. However, to the best of our knowledge, a quantitative analysis of the performance and characteristics of the different heuristics to solve this problem has never been done before. For this reason, in this work, we provide a detailed study of the different state-of-the-arts methods for structural learning on simulated data considering both BNs with discrete and continuous variables, and with different rates of noise in the data. In particular, we investigate the characteristics of different widespread scores proposed for the inference and the statistical pitfalls within them.

Learning DAG or Bayesian network models is an important problem in multi-variate causal inference. However, a number of challenges arises in learning large-scale DAG models including model identifiability and computational complexity since the space of directed graphs is huge. In this paper, we address these issues in a number of steps for a broad class of DAG models where the noise or variance is signal-dependent. Firstly we introduce a new class of identifiable DAG models, where each node has a distribution where the variance is a quadratic function of the mean (QVF DAG models). Our QVF DAG models include many interesting classes of distributions such as Poisson, Binomial, Geometric, Exponential, Gamma and many other distributions in which the noise variance depends on the mean. We prove that this class of QVF DAG models is identifiable, and introduce a new algorithm, the OverDispersion Scoring (ODS) algorithm, for learning large-scale QVF DAG models. Our algorithm is based on firstly learning the moralized or undirected graphical model representation of the DAG to reduce the DAG search-space, and then exploiting the quadratic variance property to learn the causal ordering. We show through theoretical results and simulations that our algorithm is statistically consistent in the high-dimensional p>n setting provided that the degree of the moralized graph is bounded and performs well compared to state-of-the-art DAG-learning algorithms.

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.

In this paper a new Bayesian model for sparse linear regression with a spatio-temporal structure is proposed. It incorporates the structural assumptions based on a hierarchical Gaussian process prior for spike and slab coefficients. We design an inference algorithm based on Expectation Propagation and evaluate the model over the real data.

The original goal of this post was to explore the relationship between the softmax and sigmoid functions. In truth, this relationship had always seemed just out of reach: "One has an exponent in the numerator! One has a 1 in the denominator!" And of course, the two have different names. Once derived, I quickly realized how this relationship backed out into a more general modeling framework motivated by the conditional probability axiom itself.

Trajectory analysis is essential in many applications. In this paper, we address the problem of representing motion trajectories in a highly informative way, and consequently utilize it for analyzing trajectories. Our approach first leverages the complete information from given trajectories to construct a thermal transfer field which provides a context-rich way to describe the global motion pattern in a scene. Then, a 3D tube is derived which depicts an input trajectory by integrating its surrounding motion patterns contained in the thermal transfer field. The 3D tube effectively: 1) maintains the movement information of a trajectory, 2) embeds the complete contextual motion pattern around a trajectory, 3) visualizes information about a trajectory in a clear and unified way. We further introduce a droplet-based process. It derives a droplet vector from a 3D tube, so as to characterize the high-dimensional 3D tube information in a simple but effective way. Finally, we apply our tube-and-droplet representation to trajectory analysis applications including trajectory clustering, trajectory classification & abnormality detection, and 3D action recognition. Experimental comparisons with state-of-the-art algorithms demonstrate the effectiveness of our approach.

Within machine learning, the supervised learning field aims at modeling the input-output relationship of a system, from past observations of its behavior. Decision trees characterize the input-output relationship through a series of nested $if-then-else$ questions, the testing nodes, leading to a set of predictions, the leaf nodes. Several of such trees are often combined together for state-of-the-art performance: random forest ensembles average the predictions of randomized decision trees trained independently in parallel, while tree boosting ensembles train decision trees sequentially to refine the predictions made by the previous ones. The emergence of new applications requires scalable supervised learning algorithms in terms of computational power and memory space with respect to the number of inputs, outputs, and observations without sacrificing accuracy. In this thesis, we identify three main areas where decision tree methods could be improved for which we provide and evaluate original algorithmic solutions: (i) learning over high dimensional output spaces, (ii) learning with large sample datasets and stringent memory constraints at prediction time and (iii) learning over high dimensional sparse input spaces.

We introduce Fisher consistency in the sense of unbiasedness as a desirable property for estimators of class prior probabilities. Lack of Fisher consistency could be used as a criterion to dismiss estimators that are unlikely to deliver precise estimates in test datasets under prior probability and more general dataset shift. The usefulness of this unbiasedness concept is demonstrated with three examples of classifiers used for quantification: Adjusted Classify & Count, EM-algorithm and CDE-Iterate. We find that Adjusted Classify & Count and EM-algorithm are Fisher consistent. A counter-example shows that CDE-Iterate is not Fisher consistent and, therefore, cannot be trusted to deliver reliable estimates of class probabilities.