Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.

Simultaneous Learning of Non-Linear Manifold and Dynamical Models for High-Dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. The model structure setup and parameter learning are done using a variational Bayesian approach, which enables automatic Bayesian model structure selection, hence solving the problem of over-fitting. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.

Multiplexing VBR Traffic Flows with Guaranteed Application-level QoS Using Statistical Rate Monotonic Scheduling

Quality of Service (QoS) guarantees are required by an increasing number of applications to ensure a minimal level of fidelity in the delivery of application data units through the network. Application-level QoS does not necessarily follow from any transport-level QoS guarantees regarding the delivery of the individual cells (e.g. ATM cells) which comprise the application's data units. The distinction between application-level and transport-level QoS guarantees is due primarily to the fragmentation that occurs when transmitting large application data units (e.g. IP packets, or video frames) using much smaller network cells, whereby the partial delivery of a data unit is useless; and, bandwidth spent to partially transmit the data unit is wasted. The data units transmitted by an application may vary in size while being constant in rate, which results in a variable bit rate (VBR) data flow. That data flow requires QoS guarantees. Statistical multiplexing is inadequate, because no guarantees can be made and no firewall property exists between different data flows. In this paper, we present a novel resource management paradigm for the maintenance of application-level QoS for VBR flows. Our paradigm is based on Statistical Rate Monotonic Scheduling (SRMS), in which (1) each application generates its variable-size data units at a fixed rate, (2) the partial delivery of data units is of no value to the application, and (3) the QoS guarantee extended to the application is the probability that an arbitrary data unit will be successfully transmitted through the network to/from the application.

A Dopamine-Acetylcholine Cascade: Simulating Learned and Lesion-Induced Behavior ff Striatal Cholinergic Interneurons

The "teaching signal" that modulates reinforcement learning at cortico-striatal synapses may be a sequence composed of an adaptively scaled DA burst, a brief ACh burst, and a scaled ACh pause. Such an interpretation is consistent with recent data on cholinergic interneurons of the striatum are tonically active neurons (TANs) that respond with characteristic pauses to novel events and to appetitive and aversive conditioned stimuli. Fluctuations in acetylcholine release by TANs modulate performance- and learning- related dynamics in the striatum. Whereas tonic activity emerges from intrinsic properties of these neurons, glutamatergic inputs from thalamic centromedian-parafascicular nuclei, and dopaminergic inputs from midbrain are required for the generation of pause responses. No prior computational models encompass both intrinsic and synaptically-gated dynamics. We present a mathematical model that robustly accounts for behavior-related electrophysiological properties of TANs in terms of their intrinsic physiological properties and known afferents. In the model balanced intrinsic hyperpolarizing and depolarizing currents engender tonic firing, and glutamatergic inputs from thalamus (and cortex) both directly excite and indirectly inhibit TANs. If the latter inhibition, probably mediated by GABAergic NOS interneurons, exceeds a threshold, its effect is amplified by a KIR current to generate a prolongued pause. In the model, the intrinsic mechanisms and external inputs are both modulated by learning-dependent dopamine (DA) signals and our simulations revealed that many learning-dependent behaviors of TANs are explicable without recourse to learning-dependent changes in synapses onto TANs.

Simulating Effects of Learning and Lesions with a Model of Intrinsic and Synaptically Gated Responses of Striatal Cholinergic Interneurons

The giant cholinergic interneurons of the striatum are tonically active neurons (TANs) that respond with characteristic pauses to novel events and to appetitive and aversive conditioned stimuli. Fluctuations in acetylcholine release by TANs modulate performance- and learning-related dynamics in the striatum. Whereas tonic activity emerges from intrinsic properties of these neurons, glutamatergic inputs from thalamic centromedian-parafascicular nuclei, and dopaminergic inputs from midbrain, are required for the generation of pause responses. No prior computational models encompass both intrinsic and synaptically-gated dynamics. We present a mathematical model that robustly accounts for behavior-related electrophysiological properties of TANs in terms of their intrinsic physiological properties and known afferents. In the model, balanced intrinsic hyperpolarizing and depolarizing currents engender tonic firing, and glutamatergic inputs from thalamus (and cortex) both directly excite and indirectly inhibit TANs. If the latter inhibition, presumably mediated by GABAergic interneurons, exceeds a threshold, its effect is amplified by a KIR current to generate a prolonged pause. In the model, the intrinsic mechanisms and external inputs are both modulated by learning-dependent dopamine (DA) signals and our simulations revealed that many learning-dependent behaviors of TANs are explicable without recourse to learning-dependent changes in synapses onto TANs. The "teaching signal" that modulates reinforcement learning at cortico-striatal synapses may be a sequence composed of an adaptively scaled DA burst, a brief ACh burst, and a scaled ACh pause. Such an interpretation is consistent with recent data on cholinergic control of LTD of cortical synapses onto striatal spiny projection neurons.