This dissertation centers on the development of Bayesian methods for learning differ- ent types of variation in switching nonlinear gene regulatory networks (GRNs). A new nonlinear and dynamic multivariate GRN model is introduced to account for different sources of variability in GRNs. The new model is aimed at more precisely capturing the complexity of GRN interactions through the introduction of time-varying kinetic order parameters, while allowing for variability in multiple model parameters. This model is used as the drift function in the development of several stochastic GRN mod- els based on Langevin dynamics. Six models are introduced which capture intrinsic and extrinsic noise in GRNs, thereby providing a full characterization of a stochastic regulatory system. A Bayesian hierarchical approach is developed for learning the Langevin model which best describes the noise dynamics at each time step. The trajectory of the state, which are the gene expression values, as well as the indicator corresponding to the correct noise model are estimated via sequential Monte Carlo (SMC) with a high degree of accuracy. To address the problem of time-varying regulatory interactions, a Bayesian hierarchical model is introduced for learning variation in switching GRN architectures with unknown measurement noise covariance. The trajectory of the state and the indicator corresponding to the network configuration at each time point are estimated using SMC. This work is extended to a fully Bayesian hierarchical model to account for uncertainty in the process noise covariance associated with each network architecture. An SMC algorithm with local Gibbs sampling is developed to estimate the trajectory of the state and the indicator correspond- ing to the network configuration at each time point with a high degree of accuracy. The results demonstrate the efficacy of Bayesian methods for learning information in switching nonlinear GRNs.

Object tracking refers to the problem of estimating a moving object's time-varying parameters that are indirectly observed in measurements at each time step. Increased noise and clutter in the measurements reduce estimation accuracy as they increase the uncertainty of tracking in the field of view. Whereas tracking is performed using a Bayesian filter, a Bayesian smoother can be utilized to refine parameter state estimations that occurred before the current time. In practice, smoothing can be widely used to improve state estimation or correct data association errors, and it can lead to significantly better estimation performance as it reduces the impact of noise and clutter. In this work, a single object tracking method is proposed based on integrating Kalman filtering and smoothing with thresholding to remove unreliable measurements. As the new method is effective when the noise and clutter in the measurements are high, the main goal is to find these measurements using a moving average filter and a thresholding method to improve estimation. Thus, the proposed method is designed to reduce estimation errors that result from measurements corrupted with high noise and clutter. Simulations are provided to demonstrate the improved performance of the new method when compared to smoothing without thresholding. The root-mean-square error in estimating the object state parameters is shown to be especially reduced under high noise conditions.

Increased demand on bandwidth has resulted in wireless communications and radar systems sharing spectrum. As signal transmissions from both modalities coexist, methodologies must be designed to reduce the induced interference from each system. This work considers the problem of tracking an object using radar measurements embedded in noise and corrupted from transmissions of multiple communications users. Radar received signals in low noise can be successively processed to estimate object parameters maximum likelihood estimation. For linear frequency-modulated (LFM) signals, such estimates can be efficiently computed by integrating the Wigner distribution along lines in the time-frequency (TF) plane. However, the presence of communications interference highly reduces estimation performance.This thesis proposes a new approach to increase radar estimation performance by integrating a highly-localized TF method with data clustering. The received signal is first decomposed into highly localized Gaussians using the iterative matching pursuit decomposition (MPD). As the MPD is iterative, high noise levels can be reduced by appropriately selecting the algorithm’s stopping criteria. The decomposition also provides feature vectors of reduced dimensionality that can be used for clustering using a Gaussian mixture model (GMM). The proposed estimation method integrates along lines of a modified Wigner distribution of the Gaussian clusters in the TF plane. Using simulations, the object parameter estimation performance of the MPD is shown to highly improve when the MPD is integrated with GMM clustering.

The field of Computer Vision has seen great accomplishments in the last decade due to the advancements in Deep Learning. With the advent of Convolutional Neural Networks, the task of image classification has achieved unimaginable success when perceived through the traditional Computer Vision lens. With that being said, the state-of-the-art results in the image classification task were produced under a closed set assumption i.e. the input samples and the target datasets have knowledge of class labels in the testing phase. When any real-world scenario is considered, the model encounters unknown instances in the data. The task of identifying these unknown instances is called Open-Set Classification. This dissertation talks about the detection of unknown classes and the classification of the known classes. The problem is approached by using a neural network architecture called Deep Hierarchical Reconstruction Nets (DHRNets). It is dealt with by leveraging the reconstruction part of the DHRNets to identify the known class labels from the data. Experiments were also conducted on Convolutional Neural Networks (CNN) on the basis of softmax probability, Autoencoders on the basis of reconstruction loss, and Mahalanobis distance on CNN's to approach this problem.

With the formation of next generation wireless communication, a growing number of new applications like internet of things, autonomous car, and drone is crowding the unlicensed spectrum. Licensed network such as LTE also comes to the unlicensed spectrum for better providing high-capacity contents with low cost. However, LTE was not designed for sharing spectrum with others. A cooperation center for these networks is costly because they possess heterogeneous properties and everyone can enter and leave the spectrum unrestrictedly, so the design will be challenging. Since it is infeasible to incorporate potentially infinite scenarios with one unified design, an alternative solution is to let each network learn its own coexistence policy. Previous solutions only work on fixed scenarios. In this work we present a reinforcement learning algorithm to cope with the coexistence between Wi-Fi and LTE-LAA agents in 5 GHz unlicensed spectrum. The coexistence problem was modeled as a Dec-POMDP and Bayesian approach was adopted for policy learning with nonparametric prior to accommodate the uncertainty of policy for different agents. A fairness measure was introduced in the reward function to encourage fair sharing between agents. We turned the reinforcement learning into an optimization problem by transforming the value function as likelihood and variational inference for posterior approximation. Simulation results demonstrate that this algorithm can reach high value with compact policy representations, and stay computationally efficient when applying to agent set.

Infants born before 37 weeks of pregnancy are considered to be preterm. Typically, preterm infants have to be strictly monitored since they are highly susceptible to health problems like hypoxemia (low blood oxygen level), apnea, respiratory issues, cardiac problems, neurological problems as well as an increased chance of long-term health issues such as cerebral palsy, asthma and sudden infant death syndrome. One of the leading health complications in preterm infants is bradycardia - which is defined as the slower than expected heart rate, generally beating lower than 60 beats per minute. Bradycardia is often accompanied by low oxygen levels and can cause additional long term health problems in the premature infant.The implementation of a non-parametric method to predict the onset of brady- cardia is presented. This method assumes no prior knowledge of the data and uses kernel density estimation to predict the future onset of bradycardia events. The data is preprocessed, and then analyzed to detect the peaks in the ECG signals, following which different kernels are implemented to estimate the shared underlying distribu- tion of the data. The performance of the algorithm is evaluated using various metrics and the computational challenges and methods to overcome them are also discussed.
It is observed that the performance of the algorithm with regards to the kernels used are consistent with the theoretical performance of the kernel as presented in a previous work. The theoretical approach has also been automated in this work and the various implementation challenges have been addressed.

The problem of multiple object tracking seeks to jointly estimate the time-varying cardinality and trajectory of each object. There are numerous challenges that are encountered in tracking multiple objects including a time-varying number of measurements, under varying constraints, and environmental conditions. In this thesis, the proposed statistical methods integrate the use of physical-based models with Bayesian nonparametric methods to address the main challenges in a tracking problem. In particular, Bayesian nonparametric methods are exploited to efficiently and robustly infer object identity and learn time-dependent cardinality; together with Bayesian inference methods, they are also used to associate measurements to objects and estimate the trajectory of objects. These methods differ from the current methods to the core as the existing methods are mainly based on random finite set theory.

The first contribution proposes dependent nonparametric models such as the dependent Dirichlet process and the dependent Pitman-Yor process to capture the inherent time-dependency in the problem at hand. These processes are used as priors for object state distributions to learn dependent information between previous and current time steps. Markov chain Monte Carlo sampling methods exploit the learned information to sample from posterior distributions and update the estimated object parameters.

The second contribution proposes a novel, robust, and fast nonparametric approach based on a diffusion process over infinite random trees to infer information on object cardinality and trajectory. This method follows the hierarchy induced by objects entering and leaving a scene and the time-dependency between unknown object parameters. Markov chain Monte Carlo sampling methods integrate the prior distributions over the infinite random trees with time-dependent diffusion processes to update object states.

The third contribution develops the use of hierarchical models to form a prior for statistically dependent measurements in a single object tracking setup. Dependency among the sensor measurements provides extra information which is incorporated to achieve the optimal tracking performance. The hierarchical Dirichlet process as a prior provides the required flexibility to do inference. Bayesian tracker is integrated with the hierarchical Dirichlet process prior to accurately estimate the object trajectory.

The fourth contribution proposes an approach to model both the multiple dependent objects and multiple dependent measurements. This approach integrates the dependent Dirichlet process modeling over the dependent object with the hierarchical Dirichlet process modeling of the measurements to fully capture the dependency among both object and measurements. Bayesian nonparametric models can successfully associate each measurement to the corresponding object and exploit dependency among them to more accurately infer the trajectory of objects. Markov chain Monte Carlo methods amalgamate the dependent Dirichlet process with the hierarchical Dirichlet process to infer the object identity and object cardinality.

Simulations are exploited to demonstrate the improvement in multiple object tracking performance when compared to approaches that are developed based on random finite set theory.