Proposes a new signal model for high-dimensional, small-sample-size data.
problem Signal detection in high-dimensional, small-sample-size datasets.
method Intrinsic signal model based on dynamical system assumption.
result Taguchi method effectively detects signals in the proposed model.
Study risk-averse insider's behavior in dynamic signal asset pricing.
problem Analyzing risk-averse insider's dynamic signal in asset pricing.
method Employing a weak conditioning methodology to construct a Schrödinger bridge, deriving necessary conditions for equilibrium.
result Derive explicit closed-form solutions for important cases.
Study on Langevin dynamics for recovering planted signals in spiked matrix models.
problem Recovering a planted signal in spiked matrix models.
method Path-wise characterization of overlap using integro-differential equations and explicit formula derivation.
result Sharp phase transition in limiting overlap: positive in one regime, zero in another due to injected noise.
Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framew…
A method uses non-autonomous equations to classify time signals efficiently.
problem Time signal classification with minimal parameters and high accuracy.
method Develops a framework using non-autonomous dynamical equations to classify time signals.
result The method achieves comparable accuracy with fewer parameters than existing methods.
Paper uses SGLD to recover signals from generative models, proving convergence under mild conditions.
problem Signal recovery from generative priors in compressed sensing.
method Stochastic Gradient Langevin Dynamics (SGLD) for signal recovery.
result SGLD converges to the true signal under mild assumptions on the generative model.
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to adapt their strategies together. This change in the environment results in dynamical…
Despite the importance of sparsity signal models and the increasing prevalence of high-dimensional streaming data, there are relatively few algorithms for dynamic filtering of time-varying sparse signals. Of the existing algorithms, fewer still provide strong performance guarantees. This paper examines two algorithms f…
Studying a softmax-attention model, we show that the learned query converges to the latent signal subspace spanned by the informative direction.
problem Understanding the theoretical principles of attention mechanisms in large-scale token collections.
method Deriving a population objective and analyzing the limiting ordinary differential equation of the learning dynamics.
result The learned query asymptotically recovers the latent signal up to the intrinsic sign ambiguity.
Dynamic econometric models improve trading signals in momentum strategies.
problem Static momentum strategies are inefficient; dynamic models enhance accuracy.
method Dynamic binary classifier model to learn time-varying momentum importance.
result Dynamic classifier outperforms traditional naive time series momentum strategy.
Dynamic model improves static economics by incorporating time effects.
problem Static economics overlooks time-dependent phenomena, limiting model accuracy.
method Signals-based approach to reinterpret microeconomic theory, using utility function.
result Dynamic models provide better comparisons with empirical observations.
Neural ODEs control graph dynamics with low energy feedback.
problem Controlling complex dynamical systems on graphs.
method Neural Ordinary Differential Equation Control (NODEC) framework.
result NODEC learns low-energy control signals for graph dynamical systems.
A reservoir computer is a complex dynamical system, often created by coupling nonlinear nodes in a network. The nodes are all driven by a common driving signal. In this work, three dimension estimation methods, false nearest neighbor, covariance and Kaplan-Yorke dimensions, are used to estimate the dimension of the res…
Bayesian approach infers signaling pathways from data.
problem Accurately understand cellular regulation processes.
method Dynamic Bayesian Network structure estimation using Markov Chain Monte Carlo.
result Efficient sampling of sparse graphs improves inference.
I propose a frequency domain adaptation of the Expectation Maximization (EM) algorithm to group a family of time series in classes of similar dynamic structure. It does this by viewing the magnitude of the discrete Fourier transform (DFT) of each signal (or power spectrum) as a probability density/mass function (pdf/pm…
Study of Langevin dynamics for tensor PCA recovery in high dimensions.
problem Recovering hidden signal vectors (spikes) from noisy Gaussian tensor observations.
method Langevin dynamics approach for nonconvex optimization.
result Sample complexity matches the single-spike case but degrades for all spikes.
Brain-computer interfaces (BCIs) have enabled prosthetic device control by decoding motor movements from neural activities. Neural signals recorded from cortex exhibit nonstationary property due to abrupt noises and neuroplastic changes in brain activities during motor control. Current state-of-the-art neural signal de…
Unified model for market dynamics, linking price and order flow.
problem Modeling market dynamics and order flow in a unified framework.
method Markovian market model driven by a hidden Brownian efficient price, signal-driven and queue-reactive models.
result Stability of mid-price around efficient price at macroscopic scale, behavior as diffusion.
DynaCor detects noisy labels by learning from corrupted training signals.
problem Label noise in real-world datasets hinders model generalization.
method DynaCor introduces label corruption to indirectly simulate noisy labels and learns to distinguish clean from noisy instances.
result DynaCor outperforms state-of-the-art competitors in noisy label detection.
Proposes TSBP for matching topological signal distributions.
problem Matching signal distributions on topological domains.
method Topological Schrödinger Bridge (TSBP) with linear topology-aware stochastic dynamics.
result Derives closed-form topological SB (TSB) for Gaussian boundary distributions.
Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution.
problem Characterizing measurement complexity for signals from any prior distribution, including the entire space.
method Characterization of measurement complexity using posterior sampling estimator for Gaussian measurements and any prior distribution.
result Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution, robust to model mismatch.
This work takes the first steps towards solving the "phaseless subspace tracking" (PST) problem. PST involves recovering a time sequence of signals (or images) from phaseless linear projections of each signal under the following structural assumption: the signal sequence is generated from a much lower dimensional subsp…
Study dynamic equilibrium with insider and general uninformed agent preferences.
problem Analyzing asymmetric information and general utility functions in a continuous-time economy.
method Introducing a new method to prove existence of a partial communication equilibrium (PCE) for agents with general utility functions.
result Identify the equilibrium price in the small and large risk aversion limits for agents with power utility.
Paper presents a new framework for optimal asset and signal combination.
problem Optimal asset and signal combination problem.
method Two-stage approach: reformulate dynamic portfolio selection problem, then use Canonical Correlation Analysis.
result Improved performance of proposed method over natural benchmarks.
New algorithms improve rank one signal estimation from noisy data.
problem Estimating a rank one signal matrix from corrupted data with rotationally invariant noise.
method Developed approximate message-passing algorithms exploiting eigenvalues and iterates denoisers.
result Achieves optimal asymptotic estimation error among iterative algorithms.
New algorithm learns switching dynamics from multiple neural signals.
problem Learning accurate switching dynamical system models from multimodal neural data.
method Unsupervised learning algorithm for multiscale switching dynamical system models.
result Switching multiscale dynamical system models outperform single-scale models in behavior decoding.
STRIC detects anomalies in time series by analyzing residual signals.
problem Anomaly detection in multivariate time series data.
method End-to-end differentiable neural network architecture with Sequential Probability Ratio Test on residuals.
result STRIC outperforms state-of-the-art methods on multiple benchmarks.
Attention mechanism combines bottom-up and top-down signals in neural networks.
problem Combining robust perception with bottom-up and top-down signals.
method Attention mechanism over modulated recurrent neural networks.
result Bidirectional information flow leads to improved performance in various tasks.
SGD quickly learns a spurious XOR feature before the signal feature, revealing learning dynamics.
problem Over-reliance on spurious correlations in neural networks trained by SGD.
method Theoretical analysis of SGD on two-layer ReLU networks trained on XOR data.
result SGD learns the spurious feature first and exponentially fast, dominating the signal feature.
Study on signal recovery from low-rank matrix with sparse noise.
problem Inference of a rank-one signal in the presence of sparse noise.
method Replica method from statistical physics, recursive distributional equations, population dynamics algorithm.
result Critical signal strength for recovery via top eigenvector identified.
This paper improves parameter estimation for autonomous systems with unmodeled dynamics.
problem Accurate parameter estimation for risk-aware autonomous systems with unmodeled dynamics.
method Spectral lines-based approach for estimating parameters of dynamic models, allowing deterministic unmodeled dynamics.
result The proposed method leads to non-asymptotic bounds on parameter estimation error, robust to unmodeled dynamics, and matches existing literature in ideal conditions.
New theory explains signal propagation in normalization-free transformers.
problem Understanding signal propagation in normalization-free transformers.
method Deriving recurrence relations for activation statistics and APJNs across layers.
result Transformers with elementwise tanh-like nonlinearities exhibit subcritical signal propagation.
We present a simple model of a non-equilibrium self-organizing market where asset prices are partially driven by investment decisions of a bounded-rational agent. The agent acts in a stochastic market environment driven by various exogenous "alpha" signals, agent's own actions (via market impact), and noise. Unlike tra…
A blindfolded LLM trading framework validates market signals without ticker memorization.
problem Ensuring LLMs trade based on genuine market understanding, not memorized data.
method Anonymize tickers and company names, verify signals through reasoning embeddings, and use PPO-DSR policy.
result Achieved Sharpe ratio of 1.40 +/- 0.22 across 20 seeds, robust in volatile markets.
Proposes a wave-constrained matrix factorization for signal learning.
problem Learning signals constrained by the wave equation.
method Wave-informed matrix factorization with global optimality guarantees.
result Proves global optimality of the proposed model in polynomial time.
Motion Code models time series dynamics with sparse approximations.
problem Challenges in time series classification and forecasting on noisy data.
method Motion Code views time series as stochastic processes, assigning unique signatures to distinct dynamics.
result Motion Code outperforms benchmarks in noisy datasets, including real-world Parkinson's disease tracking.
Improved robust latent variable estimation for neural dynamics.
problem Inconsistent results due to noise and nonlinearity in existing models.
method Probabilistic approach to latent variable estimation in decomposed models.
result More accurate latent variable inference in nonlinear systems with diverse noise conditions.
Due to the dynamic nature, chaotic time series are difficult predict. In conventional signal processing approaches signals are treated either in time or in space domain only. Spatio-temporal analysis of signal provides more advantages over conventional uni-dimensional approaches by harnessing the information from both …
This study uses high-frequency data to identify early warning signals for bank crises.
problem Identifying early warning signals for impending bank crises.
method Constructing multiple recurrence networks (MRNs) based on high-frequency stock returns to monitor nonlinear dynamics.
result Key indicators of MRNs, particularly average mutual information, provide valuable insights into periods of extreme volatility.
Estimates system parameters from a single observation using kernel-based score.
problem Estimating parameters of a dynamical system from a high-dimensional signal.
method Kernel-based score to compare temporal dependencies between signal and model.
result Accuracy and efficiency demonstrated on chaotic systems.
Optimal trading is a recent field of research which was initiated by Almgren, Chriss, Bertsimas and Lo in the late 90's. Its main application is slicing large trading orders, in the interest of minimizing trading costs and potential perturbations of price dynamics due to liquidity shocks. The initial optimization frame…
While recent progress in deep reinforcement learning has enabled robots to learn complex behaviors, tasks with long horizons and sparse rewards remain an ongoing challenge. In this work, we propose an effective reward shaping method through predictive coding to tackle sparse reward problems. By learning predictive repr…
Deep reinforcement learning improves trading performance with predictable returns.
problem Improving trading performance in financial markets with low signal-to-noise ratio.
method Investigates model-free deep reinforcement learning traders in a market with known mean-reverting factors.
result DRL agents outperform benchmarks in misspecified price dynamics and extreme events.
There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has unique advantages depending on the system of interest and the application goals. I…
Signals are geometric submanifolds with specific properties.
problem Defining and analyzing signals as geometric objects.
method Defining signals as submanifolds, defining energy, and introducing a Fourier transform.
result Inequalities illustrating properties of signal energy.
New method detects dynamical system changes in time series data.
problem Detecting changes in time series data structures.
method Weighted Ordinal Partition Network (OPN) with topological data analysis (TDA).
result Improved accuracy and resilience to noise in dynamic state detection.
Study finds non-monotonic Value of Information in dynamic multi-market monopoly.
problem Investigates non-monotonicity in Value of Information for a price-setting monopolist.
method Uses a Bayesian inverse problem with Kalman-Bucy-Stratonovich filter in a dynamic discrete model.
result Non-monotonic relationship between signal variance and Value of Information.
Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel…