Embedded ensembles improve neural network performance efficiently.
problem Improving neural network performance with fewer resources.
method Analyzing the wide network limit of gradient descent dynamics using Neural-Tangent-Kernel.
result Embedded ensembles exhibit two regimes: independent and collective, affecting performance.
Generative model identifies temporal count data components with regime-dependent contributions.
problem Modeling temporal count data with regime-dependent dynamics.
method Generative framework combining regime-adaptive dynamics with Poisson log-normal emissions.
result Established identifiability of the model and revealed co-variation patterns and regime shifts.
Model predicts risk-adjusted returns across various financial markets.
problem Stationary models fail in predicting risk-adjusted returns due to market regime changes.
method Asset-independent regime-switching model using hidden Markov models.
result Accurately detects bull, bear, and high volatility periods for improved risk-adjusted returns.
In this paper analytic formulas for electricity derivatives are calculated. To this end, we assume that electricity spot prices follow a 3-regime Markov regime-switching model with independent spikes and drops and periodic transition matrix. Since the classical derivatives pricing methodology cannot be used in case of …
RAMBO optimizes multi-regime problems by discovering and modeling distinct energy basins.
problem Multi-regime problems in molecular conformation and drug discovery.
method Dirichlet Process Mixture of Gaussian Processes with adaptive hyperparameters and concentration parameters.
result Consistent improvements over state-of-the-art on multi-regime objectives.
Researchers adaptively analyze market regimes to reveal investor behavior shifts.
problem Market relationships shift across different regimes, affecting investor behavior.
method Combining Kalman filtering, Markov-switching, and asymmetric response estimation.
result Foreign investors' predictive power increases during crises, while individual investors react more strongly to positive shocks.
New model identifies regimes in non-stationary data.
problem Identifying latent regimes in non-stationary systems with instantaneous effects.
method Identifiable Markov Switching Models with exponential family noise.
result Established identifiability of latent regimes and causal structures.
We study a phenomenological model for the continuous double auction, equivalent to two independent M/M/1 queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior …
Study optimal portfolios in a non-Markovian regime-switching model with random time horizon.
problem Optimal portfolio selection in a market with non-Markovian regime-switching and random time horizon.
method Formulated as a constrained stochastic linear-quadratic optimal control problem, derived closed-form expressions for optimal portfolios and efficient frontier.
result Closed-form expressions for optimal portfolios and efficient frontier derived under non-Markovian regime-switching and random time horizon.
We consider the stochastic linear (multi-armed) contextual bandit problem with the possibility of hidden simple multi-armed bandit structure in which the rewards are independent of the contextual information. Algorithms that are designed solely for one of the regimes are known to be sub-optimal for the alternate regime…
New algorithm ensures global convergence in deep neural networks beyond NTK regime.
problem Existing global convergence guarantees do not apply to practical deep networks.
method Proposes an algorithm with global convergence guarantees under the expressivity condition.
result Algorithm ensures global convergence in practical settings beyond NTK regime.
Study finds multiple solutions for Gross-Pitaevskii equations on curved spaces.
problem Finding multiple solutions for Gross-Pitaevskii equations on Riemannian manifolds.
method Critical point theory and Γ-convergence for Ginzburg-Landau functionals, plus new isoperimetric results.
result Lower bounds on the multiplicity of solutions in terms of the topology of the velocity set.
This paper proposes a multi-scale Markov-Switching GARCH model for EUR/USD volatility.
problem Non-stationary financial volatility requires models that capture changing market conditions across multiple timescales.
method Triple-timeframe Markov-Switching GARCH (MS-GARCH) framework with AR(1)-MS-GARCH models and TVTP for short horizons.
result The proposed model produces statistically distinct regimes and superior volatility forecasting performance.
This paper aims at justifying LWF and AMP chain graphs by showing that they do not represent arbitrary independence models. Specifically, we show that every chain graph is inclusion optimal wrt the intersection of the independence models represented by a set of directed and acyclic graphs under conditioning. This impli…
New algorithms reduce regret in online MDPs by adapting to data and variance.
problem Adapting to both adversarial and stochastic environments in online MDPs.
method Develops algorithms based on global optimization and policy optimization, using optimistic follow-the-regularized-leader with log-barrier regularization.
result Achieves refined data-dependent and variance-dependent regret bounds.
We present a new method for the separation of superimposed, independent, auto-correlated components from noisy multi-channel measurement. The presented method simultaneously reconstructs and separates the components, taking all channels into account and thereby increases the effective signal-to-noise ratio considerably…
The paper optimizes portfolios using a new GARCH model with regime switching and tempered stable innovations.
problem Mitigating left tail risk in multi-asset portfolios.
method Proposes a Markov regime-switching GARCH model with multivariate normal tempered stable innovation (MRS-MNTS-GARCH) for portfolio optimization.
result Optimal portfolios with tail risk measures outperform standard deviation-based portfolios and equally weighted portfolios in various performance metrics.
In simulations of some economic gas-like models, the asymptotic regime shows an exponential wealth distribution, independently of the initial wealth distribution given to the system. The appearance of this statistical equilibrium for this type of gas-like models is explained in a rigorous analytical way.
This paper presents the solution to a European option pricing problem by considering a regime-switching jump diffusion model of the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure jump process, driving the values of interest rate and volatility coefficient. The p…
Paper proposes a differentially private test for joint dependence among random vectors.
problem Detecting joint dependence among sensitive data while maintaining privacy.
method Differentially private permutation methodology for dHSIC test.
result Proposed test attains minimax optimal power across privacy regimes.
Analyzes geodesic lengths in sparse networks, deriving a distribution.
problem Understanding connectivity and robustness in networked systems.
method Analytic derivation of geodesic length distribution in sparse networks.
result Simple closed-form expression for geodesic length distribution.
This work forecasts electricity prices using Bayesian regime detection and conditional neural processes.
problem Forecasting electricity prices with optimal operational outcomes.
method Bayesian regime detection with conditional neural processes, integrating multi-criteria decision support.
result R-NP model outperformed other models in comprehensive operational utility assessments.
Study identifies three quantization regimes for ReLU networks.
problem Approximation of Lipschitz functions by ReLU networks with finite-precision weights.
method Established through nonasymptotic tight lower and upper bounds on minimax approximation error.
result Memory-optimality achieved in proper quantization regime for deep networks.
Sine activation functions enable two-layer neural networks to learn modular addition more efficiently.
problem Learning modular addition with two-layer neural networks.
method Introduced and analyzed sine activation functions, providing theoretical and empirical evidence.
result Sine activation functions allow for constant-width network realizations of modular addition, whereas ReLU networks require linear width scaling.
Leveraged ETFs can outperform their targets in certain market conditions, contrary to the volatility drag hypothesis.
problem The long-term performance decay of leveraged ETFs due to volatility drag.
method Unified framework incorporating AR(1) and AR-GARCH models, continuous-time regime switching, and flexible rebalancing frequencies.
result Return dynamics, including return autocorrelation, volatility clustering, and regime persistence, determine LETF performance.
Markovian RNN adapts to nonstationary data using HMM for better time series prediction.
problem Nonstationary sequential data in real-life applications.
method Markovian RNN with HMM for regime switching and end-to-end optimization.
result Significant performance gains over vanilla RNN and Markov Switching ARIMA.
Recent work by Jacot et al. (2018) has shown that training a neural network using gradient descent in parameter space is related to kernel gradient descent in function space with respect to the Neural Tangent Kernel (NTK). Lee et al. (2019) built on this result by establishing that the output of a neural network traine…
Improves decision complexity in hybrid environments.
problem Complexity in hybrid decision-making problems.
method General extension of DEC framework, model aggregation approach.
result Improved regret bounds for linear Q*/V* MDPs.
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process samples are assumed uncorrelated over time and having a time-varying marginal dist…
New algorithms test independence with fewer samples by using predictive information.
problem Testing independence of distributions with limited samples.
method Augmented distribution testing framework that incorporates predictive information.
result Optimal sample complexity achieved, matching lower bounds.
Exact tail probability bounds for bounded kurtosis.
problem Determining worst-case tail probabilities under kurtosis constraints.
method AI-guided search and certifying pipeline to compute bounds.
result A four-regime map of tail probabilities with explicit formulas.
In a market with a rough or Markovian mean-reverting stochastic volatility there is no perfect hedge. Here it is shown how various delta-type hedging strategies perform and can be evaluated in such markets in the case of European options. A precise characterization of the hedging cost, the replication cost caused by th…
Develops a Best-of-Both-Worlds algorithm for linear contextual bandits with Tsallis entropy.
problem Linear contextual bandits with i.i.d. contexts.
method Follow-The-Regularized-Leader (FTRL) with Tsallis entropy.
result Achieves $O\left(\log(T)^{\frac{1+β}{2+β}}T^{\frac{1}{2+β}}
ight)$ regret under margin condition.
We find the exact worst-case tail probability for bounded kurtosis.
problem Determining the worst-case tail probability under bounded kurtosis constraints.
method AI-guided search and certificate verification around the certifying pipeline.
result A four-regime map of tail probabilities with explicit formulas and dual certificates.
We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower bound of order Ω(klogp), for directed graphs of p nodes, and at most k…
The Gauss-Newton method is analyzed for neural networks using Riemannian optimization techniques.
problem Training neural networks with smooth activations and convergence rates.
method Riemannian optimization perspective, analyzing the Gauss-Newton method in both underparameterized and overparameterized regimes.
result Geometric convergence rates independent of conditioning and eigenvalues, demonstrating accelerated convergence.
This paper studies the problem of nonparametric estimation of a smooth function with data distributed across multiple machines. We assume an independent sample from a white noise model is collected at each machine, and an estimator of the underlying true function needs to be constructed at a central machine. We place l…
We investigate the waiting-time distribution of the absolute return in the Korean stock-market index KOSPI. We define the waiting time as a time interval during which the normalized absolute return remains continuously below a threshold rc. Through an exponential bin plot, we observe that the waiting-time distributi…
Paper analyzes weak-to-strong generalization in CNNs, identifying data-scarce and data-abundant regimes.
problem Weak-to-strong generalization in CNNs trained on weak models.
method Formal analysis of gradient descent dynamics in data-scarce and data-abundant regimes.
result Identifies two regimes and distinct mechanisms of generalization in each.
Kernel methods and MLPs perform similarly to linear models in high dimensions.
problem Understanding the performance of kernel methods and MLPs in high-dimensional settings.
method Analysis of kernel methods and MLPs in a high-dimensional regime with proportional asymptotics.
result Linear models are optimal in high-dimensional settings when data is generated by kernel models with nonlinear relationships.
This thesis applies entropy as a model independent measure to address three research questions concerning financial time series. In the first study we apply transfer entropy to drawdowns and drawups in foreign exchange rates, to study their correlation and cross correlation. When applied to daily and hourly EUR/USD and…
DOODL learns shared spectral dynamics across related dynamical systems.
problem Learning independent dynamical operators for each system limits discovery of shared structure.
method DOODL learns a dictionary of characteristic spectral dynamics on a manifold of related systems.
result DOODL achieves errors one to two orders of magnitude lower than independent operator estimation methods.
A fast method for decentralized non-convex optimization over networks.
problem Decentralized non-convex optimization problems over a network of nodes.
method GT-SAGA, a randomized incremental gradient method that evaluates one component gradient per node per iteration.
result GT-SAGA achieves almost sure and mean-squared convergence to a first-order stationary point for general smooth non-convex problems.
We discuss a general method to learn data representations from multiple tasks. We provide a justification for this method in both settings of multitask learning and learning-to-learn. The method is illustrated in detail in the special case of linear feature learning. Conditions on the theoretical advantage offered by m…
In the last two decades, unsupervised latent variable models---blind source separation (BSS) especially---have enjoyed a strong reputation for the interpretable features they produce. Seldom do these models combine the rich diversity of information available in multiple datasets. Multidatasets, on the other hand, yield…
Local Gradient Descent with local steps converges to the centralized model in the interpolation regime.
problem Understanding the implicit bias of Local Gradient Descent in the interpolation regime.
method Analyzing the implicit bias of Local Gradient Descent for classification tasks with linearly separable data.
result The aggregated global model from Local-GD converges exactly to the centralized model in the interpolation regime.
We develop a mean-field theory for multi-component ICA in high dimensions.
problem Understanding multi-component ICA in high-dimensional settings.
method Asymptotically exact mean-field theory for multi-component online ICA.
result Explicit learnability boundaries and competition conditions linking step size, data moments, and initialization.
The private car license plates issued in Shanghai are bestowed the title of "the most expensive sheet iron all over the world", more expensive than gold. A citizen has to bid in an monthly auction to obtain a license plate for his new private car. We perform statistical analysis to investigate the influence of the mini…