Optimal estimator derived for partially observable LTI systems.
problem Optimal estimator for partially observable LTI systems.
method State-space representation for derivation of optimal estimator.
result Derivation of minimum error variance estimator for partially observable LTI systems.
PAC-Bayesian bounds for stochastic LTI systems derived.
problem Error bounds for stochastic LTI systems.
method PAC-Bayesian theory applied to autonomous stochastic LTI models.
result Error bounds for stochastic LTI systems derived.
Paper derives an error bound for stochastic LTI systems.
problem Stochastic LTI systems with inputs in control engineering and econometrics.
method PAC-Bayesian-Like error bound derivation.
result Derived an error bound for stochastic LTI systems.
Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
problem Estimating parameters of LTI models with non-asymptotic error bounds.
method Sharp non-asymptotic lower bounds using Cramér-Rao and van Trees inequalities, concentration results, and differential geometric constructions.
result Sharp and rate-optimal lower bounds for mean square estimation risk.
The paper tackles estimation of hidden state LTI systems of unknown order.
problem Estimation of Markov parameters and minimal realization of unknown order LTI systems.
method Hankel penalized least square estimator, Ho-Kalman algorithm, and a combined algorithm.
result Statistical guarantees for estimation error, rank recovery, and sample complexity.
New model stabilizes asynchronous LTI systems, independent of synchronous stability.
problem Stability of asynchronous LTI systems under randomization and asynchrony.
method Introduced a new model for random asynchronous LTI systems and developed a method for system identification.
result Stability of random asynchronous LTI systems is independent of synchronous stability.
HOPE improves SSMs for long-memory tasks with robust initialization and training.
problem Improving state-space models for long-memory tasks with robust initialization and training.
method Developed a new parameterization scheme called HOPE using Hankel operators and Markov parameters.
result HOPE improves SSMs' performance on Long-Range Arena tasks and demonstrates non-decaying memory.
Paper derives PAC-Bayesian bounds for LTI systems learning from empirical data.
problem Characterizing predictive power of LTI systems learned from data.
method PAC-Bayesian bounds for LTI stochastic dynamical systems with inputs.
result Finite-sample error bounds for learning algorithms of LTI systems.
A distributed system identification method for LTI systems using reverse experience replay.
problem Online system identification of LTI systems over multi-agent networks.
method DSGD-RER, a distributed variant of SGD-RER with backward updates.
result The estimation error decreases as the network size grows.
SSMs have a built-in bias towards low-frequency components, which can be adjusted.
problem Frequency bias in SSMs affects their performance on long-range sequences.
method Proposed two mechanisms to tune frequency bias: scaling initialization or applying a Sobolev-norm-based filter.
result Tuning frequency bias improves SSMs' performance on long-range sequence learning tasks.
Polynomial-time reachability for LTI systems with TLL NN controllers is achieved.
problem Bounding the reachable set of LTI systems controlled by TLL NN controllers.
method Polynomial-time computation of exact one-step reachable set and tight bounding box via two methods.
result Exact reachability computation in polynomial time for TLL NN controllers.
Complex frequency generalizes eigenvalues in LTI systems.
problem Characterizing dynamics of signals with complex values.
method Geometric frequency interpretation and transformation analysis.
result Complex frequencies in LTI systems match eigenvalues.
KKR uses Koopman theory to improve forecasting in complex systems.
problem Forecasting complex, nonlinear dynamical systems in decision-making.
method Derives a universal Koopman-invariant RKHS for LTI dynamical systems.
result KKR framework provides convergence results and generalization error bounds.
The paper sets sample complexity bounds for identifying LTI systems from a finite set.
problem Identifying an LTI system from a finite set of possible systems using trajectory data.
method Maximum likelihood estimator and information theory tools.
result Upper and lower bounds for sample complexity are derived, independent of stability assumption.
Solves parameter non-identifiability in Bayesian LTI system identification.
problem Parameter non-identifiability in standard Bayesian approaches for LTI system identification.
method Embedding canonical forms of LTI systems within the Bayesian framework.
result Unlocking the use of meaningful priors and robust uncertainty estimates.
We consider the problem of learning a realization for a linear time-invariant (LTI) dynamical system from input/output data. Given a single input/output trajectory, we provide finite time analysis for learning the system's Markov parameters, from which a balanced realization is obtained using the classical Ho-Kalman al…
Physics-based framework improves building energy forecasting.
problem Lack of physical correspondence in machine learning models for building energy systems.
method Combines LTI SSMs with subspace-based domain adaptation (SDA).
result Physics-derived subspaces align with data-derived subspaces for better forecasting.
New algorithm optimizes linear system estimation from single trajectory.
problem Estimating LTI systems from a single trajectory.
method SGD with Reverse Experience Replay (SGD−RER) result Optimal guarantees for parameter and prediction errors.
In this paper, we provide a unified analysis of temporal difference learning algorithms with linear function approximators by exploiting their connections to Markov jump linear systems (MJLS). We tailor the MJLS theory developed in the control community to characterize the exact behaviors of the first and second order …
On-line detection of anomalies in time series is a key technique used in various event-sensitive scenarios such as robotic system monitoring, smart sensor networks and data center security. However, the increasing diversity of data sources and the variety of demands make this task more challenging than ever. Firstly, t…
This systemic risk paper introduces inhomogeneous random financial networks (IRFNs). Such models are intended to describe parts, or the entirety, of a highly heterogeneous network of banks and their interconnections, in the global financial system. Both the balance sheets and the stylized crisis behaviour of banks are …
The focal point of this paper is the issue of "drawdown" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to subsequent lows. Motivated by the fact that this issue is of paramount concern to co…
Transformers can approximate Kalman Filtering in linear systems with small error.
problem Approximating Kalman Filtering using Transformers for linear dynamical systems.
method Two-step reduction: 1) Softmax self-attention block approximates Nadaraya-Watson kernel smoothing, 2) This estimator approximates Kalman Filter.
result Constructs a Transformer that implements the Kalman Filter with small additive error, uniformly bounded in time.
The Expectation-Maximization (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyze a generalized EM (GEM) algorithm in the context of Gaussian mixture models, where the maximization step in t…
Study online control of unknown time-varying systems with negative and positive results.
problem Online control of time-varying systems with unknown dynamics.
method Algorithmic upper bounds and lower bounds for different policy classes.
result Sublinear adaptive regret bounds for Disturbance Response policies.
A new FFT-based method simplifies causal structure recovery for linear dynamical systems.
problem Efficiently identifying dynamic causal effects from time-series data.
method FFT-based approach to reduce computational complexity to O(Tn3logN). result Significant computational advantage for graph reconstruction.
This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into account their sparse nature. Assuming that the system is stable, or that it is eq…
Unified Bayesian framework for LTV system identification using neural networks and Gaussian Processes.
problem Identifying Linear Time-Varying systems from input-output data.
method Bayesian modeling of impulse response as a stochastic process, using neural networks and Gaussian Processes for inference.
result Framework can infer LTI system properties from a single noisy input-output pair, achieving lower error than classical methods.
New insights into spectral statistics of sample covariance matrix for stable linear systems.
problem Estimating high-dimensional stable state transition matrices from noisy data.
method Combining spectral theorem for non-Hermitian operators, concentration of measure, and perturbation theory.
result The spectral radius of the sample covariance matrix exhibits phase transitions in high dimensions.
The paper develops a state-space approach to deep Gaussian processes for efficient state estimation.
problem Efficient regression and state estimation for deep Gaussian processes.
method Hierarchical transformed Gaussian process priors, state-space representation, linear stochastic differential equations, sequential methods.
result The state-space approach enables efficient state estimation and regression for deep Gaussian processes.
State-space systems generate probabilistic dependencies between inputs and outputs.
problem Understanding probabilistic dependencies in state-space systems.
method Introducing a probabilistic framework and proving sufficient conditions for output existence and uniqueness.
result State-space systems can generate probabilistic dependencies, even without functional relations.
A new method learns state and proposal dynamics in state-space models using neural networks.
problem Inference in non-linear state-space models.
method StateMixNN method using neural networks for proposal and transition distributions.
result Significantly improved recovery of hidden state, especially in highly non-linear scenarios.
Empirical mode modeling improves state-space analysis of noisy data.
problem Analyzing nonlinear systems with noisy data.
method Combining empirical mode decomposition with empirical dynamic modeling.
result Empirical mode modeling enhances state-space representations in noisy data.
Entropy regularization is used to get improved optimization performance in reinforcement learning tasks. A common form of regularization is to maximize policy entropy to avoid premature convergence and lead to more stochastic policies for exploration through action space. However, this does not ensure exploration in th…
Deep learning enhances active inference for dynamic state spaces.
problem Limited applicability of active inference to continuous state spaces.
method Use of deep learning to approximate probability distributions for active inference.
result Active inference can be applied to continuous state spaces.
This paper simplifies OPE in large state spaces using state abstractions.
problem Accurately evaluating policies offline in large state spaces.
method Developed a backward-model-irrelevance condition and an iterative state abstraction procedure.
result Deeply-abstracted states substantially simplify OPE sample complexity.
Predicts cryptocurrency prices with deep state-space model.
problem Predicting day-ahead crypto-currency prices.
method Proposes a deep state-space model combining state-space formulation and deep neural networks.
result The deep state-space model outperforms state-of-the-art and classical methods in accuracy.
Divides state space into regions with identical term structure shapes.
problem Classifying term structure shapes in the two-factor Vasicek model.
method Using envelopes and winding numbers to divide and classify the state space.
result Nearly complete classification of parameter space regarding term structure shapes.
Adversarial attacks on probabilistic state-space models affect latent state and policy decisions.
problem Robust reinforcement learning under adversarial observability.
method Analyzing adversarial attacks on linear probabilistic state-space models.
result Demonstrating the influence of adversarial observations on latent state and policy decisions.
Active learning selects inputs for GPSSM to learn latent states.
problem Optimally learn latent states of a GPSSM through active selection of inputs.
method Use mutual information to select informative inputs; approximate mutual information for GPSSM.
result Effective active learning of GPSSM dynamics in physical systems.
Parameterized state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand the dynamical features of the input driving time series that are formed in the sta…
State spaces of multifactor approximations of nonnegative Volterra processes are linear transformations of the nonnegative orthant.
problem Characterizing state spaces of multifactor approximations of nonnegative Volterra processes.
method Explicit linear transformation of the nonnegative orthant.
result State spaces of multifactor approximations of nonnegative Volterra processes are given by explicit linear transformation of the nonnegative orthant.
New model for insurance states using Markov jump processes with non-countable state space.
problem Modeling insurance states with non-countable state spaces.
method Developed a new Thiele's differential equation for continuous time rehabilitation rates.
result Allows for consistent calculation of reserves in disability insurance.
Structured State-Space Duality connects SSMs to masked attention.
problem Connecting SSMs and attention mechanisms for efficient modeling.
method Formalizing and generalizing SSD from scalar-identity to diagonal state matrices.
result Diagonal SSMs match training complexity lower bounds and support richer dynamics.
D-LinOSS models learn to dissipate energy, improving performance on long-range tasks.
problem Representational limitations of LinOSS models in long-range reasoning.
method Introducing Damped Linear Oscillatory State-Space models (D-LinOSS) that learn to dissipate latent state energy on arbitrary time scales.
result D-LinOSS consistently outperforms previous LinOSS methods on long-range learning tasks, achieving faster convergence and reducing hyperparameter search space.
Bayesian model detects altered neural circuits in MCI patients.
problem Detecting altered neural circuits in Mild Cognitive Impairment patients.
method Hierarchical Bayesian recurrent state space model.
result Model discovers latent states predominantly observed in MCI patients.
New method for state inference in state-space models with unknown dynamics.
problem State inference in state-space models with computationally expensive and undefined dynamics.
method Estimate state transition dynamics using a multi-output Gaussian process and Bayesian Neural Network as a surrogate model.
result Significant improvement in accuracy for state inference and prediction in non-stationary user models.
We consider the problem of learning low-dimensional representations for large-scale Markov chains. We formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, called the kernel space. The kernel space contains a set of meta states which are desired …