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…
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48 results for “single realization”
New method tests independence with single nonstationary time series.
problem Testing independence in nonstationary nonlinear time series.
method Time-varying nonlinear regression, local long-run covariance estimation, strong Gaussian approximation.
result First framework for conditional independence testing with a single realization of a nonstationary nonlinear process.
In this paper we present detailed simulation results on the wealth distribution model with quenched saving propensities. Unlike other wealth distribution models where the saving propensities are either zero or constant, this model is not found to be ergodic and self-averaging. The wealth distribution statistics with a …
We study a recent model of collaborative PAC learning where players with different tasks collaborate to learn a single classifier that works for all tasks. Previous work showed that when there is a classifier that has very small error on all tasks, there is a collaborative algorithm that finds a single classifi…
New algorithms estimate Q-functions under partial coverage and realizability, improving offline RL guarantees.
problem Offline RL with limited exploration and assumptions about data coverage and Q-function realizability.
method Proposes minimax learning algorithms to estimate soft or vanilla Q-functions with -convergence guarantees.
result PAC guarantees for offline RL under partial coverage and realizability conditions.
Paper tackles offline RL with weak assumptions on both function classes and data coverage.
problem Achieve sample-efficient offline RL with weak assumptions on both factors.
method Simple algorithm based on primal-dual formulation of MDPs, with density-ratio function modeling dual variables.
result Polynomial sample complexity achieved under realizability and single-policy concentrability.
Study on Legendrian and transverse realizations of negative torus knots.
problem Classification of transverse and Legendrian realizations of negative torus knots.
method Analysis of contact structures, knot Floer homology, Legendrian surgeries.
result Classification of strongly non-loose transverse and Legendrian realizations.
Study detects P-type bifurcations in single system realizations using unreliable kernel density estimates.
problem Detecting P-type bifurcations in signals with unreliable kernel density estimates.
method Create persistence diagrams from single system realization, statistically analyze resulting set, compare point process modeling methods.
result Subsampling outperforms other point process modeling methods in predicting P-type bifurcations.
Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through rules: high-level principles that reveal invariances within similar yet diverse examples. Under a probabilistic setting for discrete input spaces, we focus …
On Query-efficient Planning in MDPs under Linear Realizability of the Optimal State-value Functioncs.LG
TensorPlan algorithm finds δ-optimal policies with poly queries under linearly realizable state-value function.
problem Efficient planning in MDPs with linearly realizable state-value function.
method TensorPlan algorithm using poly simulator queries.
result First algorithm with polynomial query complexity using only linear-realizability of a single competing value function.
Paper finds shortest geodesic paths on hyperbolic surfaces.
problem Finding the shortest geodesic paths on hyperbolic surfaces.
method Analyzes genus g hyperbolic surfaces to find minimal length geodesics.
result Minimal geodesic length is realized by a specific polygon.
TKFT models computation via smooth vector fields, simulating functions in a single dynamical step.
problem Modeling computation in a single step.
method Established Topological Kleene Field Theory (TKFT) as a new model of computation.
result Any computable function can be simulated in a single go of a dynamical system.
Researchers solve Nielsen Realization problems for K3 surfaces in various categories.
problem Realizing finite groups of mapping classes as diffeomorphisms, isometries, or automorphisms in K3 surfaces.
method Introduced a computable invariant and constructed an action by isometries.
result Some finite groups are realizable while others are not, depending on preserved structures.
Study online learning with set-valued feedback, showing differences between deterministic and randomized approaches.
problem Online learning with set-valued feedback, where labels are sets rather than single labels.
method Introduced new combinatorial dimensions (Set Littlestone and Measure Shattering) to characterize learnability.
result Characterized deterministic and randomized online learnability, and established bounds for various learning settings.
The paper studies multi-curve interest rate models and their consistency and finite-dimensional realizations.
problem Consistency and existence of finite-dimensional realizations for multi-curve interest rate models.
method Geometric approach, characterizing consistency and existence of finite-dimensional realizations for multi-curve models.
result Characterization of consistency and existence of finite-dimensional realizations for multi-curve models.
This paper tackles deferral learning with multiple experts, providing strong theoretical guarantees.
problem Optimizing input assignment to experts balancing accuracy and computational cost.
method Introducing new surrogate loss functions and efficient algorithms with strong theoretical learning guarantees.
result Realizable -consistency, -consistency bounds, and Bayes-consistency for deferral learning.
Fitting models for non-Poisson point processes is complicated by the lack of tractable models for much of the data. By using large samples of independent and identically distributed realizations and statistical learning, it is possible to identify absence of fit through finding a classification rule that can efficientl…
Investigates the benefits of multi-head attention in Transformers, deriving convergence and generalization guarantees.
problem Underexplored dynamics of multi-head attention in Transformer training and generalization.
method Derives convergence and generalization guarantees for gradient-descent training of a multi-head self-attention model.
result Establishes conditions for initialization that ensure multi-head attention's realizability.
For any unoriented loop on a compact connected oriented surface with one boundary component, the generalized Dehn twist along the loop is defined as an automorphism of the completed group ring of the fundamental group of the surface. If the loop is simple, this is the usual right handed Dehn twist, in particular realiz…
We propose two neural network based mixture models in this article. The proposed mixture models are explicit in nature. The explicit models have analytical forms with the advantages of computing likelihood and efficiency of generating samples. Computation of likelihood is an important aspect of our models. Expectation-…
For a hyperbolic 3-manifold with a torus boundary component,all but finitely many Dehn fillings yield hyperbolic 3-manifolds. In this paper, we will focus on the situation where has two exceptional Dehn fillings: an annular filling and a toroidal filling. For such situation, Gordon gave an upper bound 5 for the…
Gradient descent struggles with learning a single neuron with bias.
problem Learning a single neuron with a bias term in the realizable setting with ReLU activation.
method Theoretical study using gradient descent, characterizing critical points, and providing convergence guarantees.
result Gradient descent faces significant challenges in learning a single neuron with bias, unlike the bias-less case.
The study examines how global economic policy uncertainty affects crude oil futures volatility.
problem Predicting crude oil futures volatility using global economic policy uncertainty.
method Established single-factor and two-factor models under the GARCH-MIDAS framework, tested with rolling-window and fixed-span specifications.
result GEPU changes have stronger predictive power than the GEPU index for crude oil futures volatility.
New efficient method for inverse Z-transform reduces complexity significantly.
problem Efficient numerical realization of inverse Z-transform for large n.
method Derives sufficient conditions for new scheme, applies to option pricing.
result Significant reduction in complexity for large n, especially for European options.
New method learns SIMs with arbitrary monotone activations without strong distributional assumptions.
problem Learning Single-Index Models with arbitrary monotone activations.
method Based on omniprediction with calibrated multiaccuracy and Bregman divergences.
result First agnostic learning result for SIMs with arbitrary monotone activations.
The problem of immersing a simply connected surface with a prescribed shape operator is discussed. From classical and more recent work, it is known that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space o…
On the concentration of large deviations for fat tailed distributions, with application to financial datacond-mat.stat-mech
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable. The regime of large deviations is separated from the regi…
Efficiently learns Single-Index Models with constant factor approximation.
problem Learning Single-Index Models under loss with unknown link functions.
method An efficient algorithm using alignment sharpness for optimization.
result Achieves constant factor approximation to optimal loss for various distributions and link functions.
Develops a framework to estimate NBA player salary ROI.
problem Measuring the relative return of player salaries in NBA.
method Five-part framework: GCP measure, SGV calculation, cash flow series, ROI calculation.
result Illustrates framework with 2022-2023 NBA data, showing top and bottom performers.
Planar graphs embedded in generic ways and realizing them as Reeb graphs of real algebraic functionsmath.AG
New method realizes planar graphs as Reeb graphs of algebraic functions.
problem Realizing planar graphs as Reeb graphs of algebraic functions.
method Generic embedding and elementary procedures.
result Generically embedded planar graphs are homeomorphic to Reeb graphs of algebraic functions.
In this paper, we introduce transformations of deep rectifier networks, enabling the conversion of deep rectifier networks into shallow rectifier networks. We subsequently prove that any rectifier net of any depth can be represented by a maximum of a number of functions that can be realized by a shallow network with a …
Many four-dimensional supersymmetric compactifications of F-theory contain gauge groups that cannot be spontaneously broken through geometric deformations. These "non-Higgsable clusters" include realizations of , , and , but no gauge groups or factors with . We study poss…
Deep neural networks can approximate complex functions through repeated compositions of a fixed-size ReLU network.
problem Understanding the expressive power of deep neural networks through function compositions.
method Demonstrated the surprising expressive power of repeated compositions of a single fixed-size ReLU network.
result Repeated compositions of a single fixed-size ReLU network can approximate 1-Lipschitz continuous functions on with an error .
Using the most comprehensive source of commercially available data on the US National Market System, we analyze all quotes and trades associated with Dow 30 stocks in 2016 from the vantage point of a single and fixed frame of reference. We find that inefficiencies created in part by the fragmentation of the equity mark…
The paper finds and visualizes unique geometric polyhedra and tori with few vertices.
problem Finding and visualizing geometric polyhedra and tori with specific vertex configurations.
method Using Schlegel diagrams and geometric realization in 3D and 4D space.
result Identifies and visualizes 12 triangulations of the 2-torus and 12 triangulations of the 2D projective plane.
Towards Unsupervised Single-Channel Blind Source Separation using Adversarial Pair Unmix-and-Remixeess.SP
Blind single-channel source separation is a long standing signal processing challenge. Many methods were proposed to solve this task utilizing multiple signal priors such as low rank, sparsity, temporal continuity etc. The recent advance of generative adversarial models presented new opportunities in signal regression …
New algorithm trains ReLU gates provably in linear time.
problem Training ReLU gates in realizable settings with mild conditions.
method Iterative stochastic algorithm with moment assumptions.
result First recovery of true labels under data-poisoning attacks.
Over-parametrization speeds up learning a single neuron model.
problem Understanding why over-parametrization accelerates learning in neural networks.
method Studied a simple model of a single teacher neuron with quadratic activation, showing how over-parametrization can lead to faster convergence.
result Over-parametrization helps gradient descent enter the neighborhood of a global optimal solution faster.
A Braid Boxmath.HO
Interactive art piece shows braid groups and plane motions.
problem Understanding braid groups and their actions.
method Interactive art piece illustrating two braid group definitions and their action on free group.
result Demonstrates all plane motions in a single subspace.
MTNPs jointly model multiple correlated tasks from various sources.
problem Naive NPs can only model a single stochastic process and infer tasks independently.
method MTNPs are a hierarchical extension of NPs that jointly infer tasks from multiple stochastic processes, considering inter-task correlation and handling incomplete data.
result MTNPs successfully model multiple tasks jointly, discovering and exploiting their correlations in various real-world data.
As adversarial attacks pose a serious threat to the security of AI system in practice, such attacks have been extensively studied in the context of computer vision applications. However, few attentions have been paid to the adversarial research on automatic path finding. In this paper, we show dominant adversarial exam…
Bayesian inference forgetting framework removes influence of single data points.
problem Enforcement of the right to be forgotten in machine learning causes high costs for companies.
method Develops forgetting algorithms for variational and Markov chain Monte Carlo in Bayesian inference.
result Proves removal of influence of single datums on learned models with guaranteed generalizability.
Paper introduces ICGNs to model convex gradients.
problem Modeling convex gradients efficiently.
method Integrates Jacobian-vector product in a neural network.
result Single layer ICGN outperforms single layer ICNN in fitting.
Finite-horizon sequential experimental design (SED) arises naturally in many contexts, including hyperparameter tuning in machine learning among more traditional settings. Computing the optimal policy for such problems requires solving Bellman equations, which are generally intractable. Most existing work resorts to se…
MTL-NAS combines NAS with GP-MTL for task-agnostic multi-task learning.
problem Designing architectures for diverse tasks with varying priors.
method Disentangled GP-MTL networks, hierarchical feature sharing, and gradient-based search.
result General-purpose model trained once can adapt to multiple tasks.
Comparative learning combines realizable and agnostic settings for two hypothesis classes, reducing sample complexity.
problem Learning with two hypothesis classes in a more general setting than single hypothesis classes.
method Introduces comparative learning, defines mutual VC dimension and Littlestone dimension, and applies insights to multiaccuracy and multicalibration.
result Sample complexity of comparative learning is characterized by mutual VC dimension and Littlestone dimension.
We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive. This answers a question of Stoimenow's in the (strong) positive. As a second main result, we give simple and complete characterizations of link diagrams with quasipositive canonical surface (the surface produced by Sei…
New method optimizes policies without assuming known link functions between preferences and rewards.
problem Policy alignment with unknown and unrestricted link functions.
method Formulates an -divergence-constrained reward maximization problem, learning policies directly.
result Induces a semiparametric single-index binary choice model for policy alignment.