Paper tackles tensor completion for 3D or higher exponential signals.
problem Recover N-dimensional exponential signals from limited data.
method Formulates as low-rank tensor completion problem, promotes exponential structure via Hankel matrix nuclear norm.
result Successfully recovers full signals from very limited samples.
Exponential smoothers are a simple and memory efficient way to compute running averages of time series. Here we define and describe practical properties of exponential smoothers for signals observed at constant and variable intervals.
New insights into how to inspect and learn from multi-stage processes and AI reasoning.
problem Understanding how to attribute outcomes to early stages in multi-stage operations and AI reasoning.
method Information-theoretic analysis and mathematical proofs of four key results.
result Uniform checkpoint spacing is minimax-optimal for inspection design under homogeneous signal attenuation.
The paper optimizes portfolios using MACD signals derived from price history.
problem Optimizing risky asset portfolios with latent mean-reverting and momentum factors.
method Derives optimal strategies based on MACD signals from EMA processes.
result Establishes admissibility and verification of optimal strategies.
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.
This paper explores robust recovery of a superposition of R distinct complex exponential functions from a few random Gaussian projections. We assume that the signal of interest is of 2N−1 dimensional and R<<2N−1. This framework covers a large class of signals arising from real applications in biology, automation,…
Deep ReLU networks can approximate various signal types with exponential error decay.
problem Approximating different signal structures with deep neural networks.
method Demonstrated approximation of polynomials, sinusoidal functions, oscillatory textures, and fractals.
result Finite-width deep ReLU networks require fewer connections than wide finite-depth networks for smooth function approximation.
Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.
problem Achieving optimal error rates in clustering sub-exponential mixture models.
method Establishes universal lower bounds and demonstrates iterative algorithms' optimality in sub-exponential mixture models.
result Iterative algorithms achieve the universal lower bound in sub-exponential mixture models.
TDA detects financial bubbles through early warning signals.
problem Detecting financial bubbles early.
method Using Log-Periodic Power Law Singularity (LPPLS) model to fit financial time series data.
result TDA generates early warning signals when LPPLS model fits the data.
Researchers discover phase transitions in estimating object ranks from pairwise interactions.
problem Estimating the underlying ranks of objects from pairwise comparisons or collaborations.
method Characterized optimal statistical error rates for various signal-to-noise ratios.
result Phase transitions between optimal error rates of polynomial, exponential, zero, and trivial.
The paper introduces a new method to identify trends in noisy signals efficiently.
problem Identifying unknown underlying trends in noisy signals, especially with abrupt changes and outliers.
method Developed the ℓ1 Adaptive Trend Filter and an enhanced coordinate descent algorithm. result The method can consistently identify components in the underlying trend and multiple level-shifts.
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.
Agents learn state without recalling private signals in networks.
problem Agents learn unknown state from private signals in networks.
method Memoryless update rules that replicate Bayesian agents' beliefs.
result Exponential learning rate similar to Bayesian agents.
New model predicts links in community-based networks robustly.
problem Link prediction in community-based networks with local clustering errors.
method Markov Stochastic Block Model (MSBM) with Hidden Markov Model (HMM) predictions.
result Misclassification error decays exponentially with relevant signal-to-noise ratio (SNR).
Investor optimizes stock investments with noisy future price signals.
problem Optimizing stock investments with uncertain future stock prices.
method Dynamic investment strategy with partial observation of Brownian motion.
result Closed-form solution for optimal investment problem.
Gaussian BP algorithm converges exponentially under walk summability for cyclic graphs.
problem Convergence rate of Gaussian BP for cyclic graphs.
method Extending known results on walk summability, proving exponential convergence rate.
result Gaussian BP converges exponentially under walk summability for cyclic graphs.
Q-Learning overestimation bias influenced by learning rate, discount factor, and reward signal.
problem Overestimation bias in Q-Learning algorithm.
method Investigated the influence of learning rate, discount factor, and reward signal on Q-Learning's overestimation bias. Tuned parameters and used an exponential moving average of reward signal.
result Q-Learning can achieve more accurate value estimates by tuning parameters and using an exponential moving average of reward signal.
SCORE improves community detection for networks with weak signals.
problem Detecting communities in networks with weak signals and severe degree heterogeneity.
method SCORE+ incorporates new features to improve SCORE's performance.
result SCORE+ achieves lower clustering errors for networks with weak signals.
Improves diffusion models by controlling total variance and signal-to-noise-ratio.
problem Long sampling time in diffusion models.
method Total-Variance/Signal-to-Noise-Ratio (TV/SNR) disentangled framework.
result Improves generation performance by controlling TV and SNR independently.
Paper studies early-stopped mirror descent for noisy sparse phase retrieval.
problem Recovering a sparse signal from noisy quadratic measurements.
method Early-stopped mirror descent with hyperbolic entropy mirror map.
result Achieves nearly minimax-optimal rate of convergence for k-sparse signals. Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
problem Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
method Reformulating Stein discrepancy construction as an explicit SNR^2 maximisation problem
result Avoiding exponential SNR^2 collapse and achieving stable SNR^2
Nuclear magnetic resonance (NMR) spectroscopy exploits the magnetic properties of atomic nuclei to discover the structure, reaction state and chemical environment of molecules. We propose a probabilistic generative model and inference procedures for NMR spectroscopy. Specifically, we use a weighted sum of trigonometric…
In this paper we present an optimization-based view of distributed parameter estimation and observational social learning in networks. Agents receive a sequence of random, independent and identically distributed (i.i.d.) signals, each of which individually may not be informative about the underlying true state, but the…
SDP achieves exponential error rate in cluster estimation for Stochastic Block Model.
problem Cluster estimation in Stochastic Block Model.
method Semidefinite Programming (SDP) formulation.
result SDP achieves exponential error rate in signal-to-noise ratio.
New algorithms recover sparse tensor principal components efficiently.
problem Recovering sparse tensor principal components from noisy data.
method Family of algorithms interpolating between polynomial-time and exhaustive search, tailored for sparse and highly sparse regimes.
result Our algorithms recover sparse vectors for signal-to-noise ratios beyond previous limits, with time complexity ildeO(np+t). New ML-based detection improves PMH signal detection in load-modulated MIMO systems.
problem Detecting PMH signals without prior CSI is challenging and computationally expensive.
method Proposes HEM-ML and HEM-KD schemes using EM and KD-tree for efficient detection.
result Achieves comparable detection results to optimal ML detector with reduced complexity.
Deep networks can compute functions with exponentially growing curvature.
problem Understanding the expressivity of deep neural networks.
method Combining Riemannian geometry and mean field theory of chaos.
result Deep networks can compute functions with exponentially growing curvature, indicating their expressivity.
Exponential neural networks store many patterns, mapping cues to targets.
problem Storing many patterns in a neural network efficiently and accurately.
method Introduced an exponential neural network with multiple layers, each storing a dataset.
result The network can store an exponential number of patterns, and it generalizes well to unseen data.
Paper tackles reinforcement learning for STL specifications with state history.
problem Learning optimal policies to satisfy STL specifications often requires too much state history, making the problem computationally intractable.
method Proposes a compact augmented state-space representation to capture state history and an approximation method to solve the objective.
result Shows the performance bound of the approximate solution and compares it with an existing technique.
A new update rule for deep reinforcement learning reduces learning variance and variance in reference signals.
problem Learning variance and incorrect reference signals in deep reinforcement learning.
method t-soft update method inspired by student-t distribution, which reduces extreme updates and accelerates similar updates.
result The t-soft update method outperforms conventional methods in terms of return and variance in PyBullet robotics simulations.
Deep learning method improves myelin water fraction estimation.
problem Estimating myelin water fraction in the brain using magnetic resonance relaxometry.
method Combines input layer regularization with automated regularization hyperparameter tuning.
result Proposed method outperforms classical methods and multi-layer perceptrons on in vivo brain data.
Estimating signals with linear recurrence relations under Gaussian noise is nearly as hard as sparse signals.
problem Estimating discrete-time signals with unknown linear recurrence relations in Gaussian noise.
method Analyzing shift-invariant subspaces and their Fourier coefficients as reproducing filters.
result The statistical complexity is nearly the same as for s-sparse signals, and the estimator is tractable. This work improves LSTM and GRU training stability and generalization.
problem Training instabilities in LSTMs and GRUs on long sequences.
method Developed a mean field theory to optimize initialization hyperparameters.
result Eliminates or reduces training instabilities and improves generalization.
Efficiently models event-based data with general parametric kernels.
problem Inference for Hawkes processes with general parametric kernels requires large datasets.
method Developed a fast ℓ2 gradient-based solver using a discretized version of events. result Improved estimation of pattern latency in brain signals.
Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced w…
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.
Optimal trading incorporates signals to reduce costs and price dynamics disruptions.
problem Minimizing trading costs and price dynamics disruptions in large orders.
method Incorporates a Markovian signal into optimal trading framework, proving existence and uniqueness of optimal strategies.
result Explicit singular optimal strategy derived for an Ornstein-Uhlenbeck signal and exponentially decaying market impact.
Functional connectivity refers to the temporal statistical relationship between spatially distinct brain regions and is usually inferred from the time series coherence/correlation in brain activity between regions of interest. In human functional brain networks, the network structure is often inferred from functional m…
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.
Hard phase in inference problems is glassy and hard to reconstruct.
problem Hard phase in inference problems that are hard to solve algorithmically.
method Study of metastable states and their entropy in low-rank matrix factorization.
result AMP algorithm performance is not improved by considering glassy states.
Proposes a privacy-preserving sign selection method for distributed systems.
problem Sign selection in distributed differentially private settings.
method Iterative peeling of stability function combined with exponential mechanism.
result Recovery of support and signs with optimal signal-to-noise ratio.
Unbiased methods for alpha-divergence minimization struggle in high dimensions.
problem The difficulty of unbiased alpha-divergence minimization in high dimensions.
method Signal-to-Noise Ratio (SNR) analysis of gradient estimators.
result The SNR of the gradient estimator worsens exponentially with dimensionality.
Proposes EMG mixture model for spectroscopy data.
problem Modeling residuals in spectroscopy data with positive support.
method Exponentially-modified Gaussian mixture (EMG) model with expectation-maximization algorithm.
result EMG mixture outperforms existing models in spectroscopy applications.
This paper examines how energy in feature maps decays in deep neural networks.
problem Understanding energy decay in deep convolutional neural networks.
method Analyzes energy conservation and decay rates in various deep neural network architectures.
result Energy in feature maps decays polynomially or exponentially across layers.
The study analyzes how neural reward models learn features for policy optimization in a Gaussian single-index model.
problem Reward modeling in policy optimization and its impact on downstream value.
method Two-stage neural reward model: first learns hidden direction, then fits readout layer.
result For any feature-learning temperature above a dimension-free threshold, a constant fraction of neurons recover the hidden direction.
Optimal trading strategy derived for nonlinear price impact models.
problem Optimal trading with nonlinear price impact induced by alpha signals.
method Variational approach, nonlinear Fredholm equation, iterative scheme.
result Existence and uniqueness of optimal trading strategy under monotonicity condition.
Improved predictive posterior density estimation through optimized importance sampling.
problem Low signal-to-noise ratio in posterior predictive densities.
method Optimized importance sampling using a test-time variational proxy.
result Significantly improved estimates of predictive posterior densities.
We consider a network of agents that aim to learn some unknown state of the world using private observations and exchange of beliefs. At each time, agents observe private signals generated based on the true unknown state. Each agent might not be able to distinguish the true state based only on her private observations.…