We provide a general framework for characterizing the trade-off between accuracy and robustness in supervised learning. We propose a method and define quantities to characterize the trade-off between accuracy and robustness for a given architecture, and provide theoretical insight into the trade-off. Specifically we in…
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
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48 results for “trade-off functions”
Study tests whether trade-off functions are above or below benchmarks using finite samples.
problem Testing trade-off functions between unknown distributions.
method Identifies a condition for nontrivial testing, constructs a test with error guarantees, and inverts the test for confidence bands.
result Finite-sample testing is possible under specific structural assumptions about rejection regions.
New trade-off found between accuracy and adversarial robustness in regression.
problem Finding a balance between accuracy and robustness in regression models.
method Deriving a fundamental trade-off between standard and adversarial risk in regression with polynomial ridge functions.
result A necessary condition for achieving adversarial robustness without significant accuracy loss.
Improved Bayesian optimisation method using randomised Gaussian process UCB.
problem Improving performance in Bayesian optimisation.
method Developed a modified Gaussian process upper confidence bound (GP-UCB) acquisition function.
result The method achieves better performance than GP-UCB in various problems.
We analyze different re-ranking algorithms for diversification and show that majority of them are based on maximizing submodular/modular functions from the class of parameterized concave/linear over modular functions. We study the optimality of such algorithms in terms of the `total curvature'. We also show that by adj…
We propose a new PAC-Bayesian bound and a way of constructing a hypothesis space, so that the bound is convex in the posterior distribution and also convex in a trade-off parameter between empirical performance of the posterior distribution and its complexity. The complexity is measured by the Kullback-Leibler divergen…
Paper develops a dynamic Bayesian approach for active learning that optimizes exploration-exploitation balance.
problem Balancing exploration and exploitation in active learning for unknown functions.
method Develops BHEEM, a Bayesian hierarchical approach with approximate Bayesian computation for sampling trade-off parameters.
result BHEEM achieves at least 21% and 11% improvement over pure exploration and exploitation strategies respectively.
New framework resolves central limit behavior in differential privacy.
problem Choosing appropriate privacy metrics in hypothesis testing.
method Infinitely divisible limit experiments and Le Cam's theory.
result Characterizes all limiting baseline trade-off functions in differential privacy.
This paper improves privacy bounds for DP algorithms using -DP.
problem Difficulty in analyzing randomness in DP algorithms due to mixture distributions.
method Derives a closed-form expression for trade-off functions and analyzes -DP.
result Enhances privacy of DP-GD with random initialization and shuffling models.
Improved neural network depth-width trade-offs via dynamical systems.
problem Expressivity of neural networks in terms of depth and width.
method Connection with dynamical systems, focusing on periodic points and Lipschitz constants.
result Sharper width lower bounds for neural networks, yielding exponential depth-width separations.
This paper compares AMMs and LOBs in exchange mechanisms, formalizing complexity vs. expressiveness trade-offs.
problem Designing efficient exchange mechanisms between assets.
method Formalizes a complexity-approximation trade-off for CFMMs and LOBs, introducing an exchange complexity measure.
result Optimally expressive mechanisms can be designed with minimal complexity, allowing for arbitrary demand curves.
Vector embedding is a foundational building block of many deep learning models, especially in natural language processing. In this paper, we present a theoretical framework for understanding the effect of dimensionality on vector embeddings. We observe that the distributional hypothesis, a governing principle of statis…
Meta-learning balances task-specific modeling and optimization complexity.
problem Balancing accurate task-specific modeling with ease of optimization in meta-learning.
method Theoretical and empirical analysis of trade-off between modeling and optimization in meta-learning.
result Explicit bounds on modeling and optimization errors for non-convex and linear regression problems.
Research explores the trade-off between multi-task learning and multitasking in deep neural networks.
problem Trade-off between multi-task learning and multitasking in deep neural networks.
method Meta-learning algorithm to manage the trade-off between shared and separated representations.
result Agent successfully optimizes training strategy based on environment.
A new convex loss function optimizes set predictions with balanced size and coverage.
problem Optimizing set predictions with balanced size and coverage.
method Proposes a convex loss function using Choquet integrals for nondecreasing subset-valued functions.
result Optimal trade-offs between conditional probabilistic coverage and set size.
Proposes a new acquisition function for batched Bayesian optimization.
problem Intractability of acquisition functions for batched Bayesian optimization.
method Statistical physics inspired acquisition function for Gaussian processes.
result Demonstrates competitive performance on various problems.
iMOCA optimizes multiple objectives with continuous approximations for resource efficiency.
problem Optimizing multiple objectives with continuous function approximations that balance accuracy and evaluation cost.
method Information-Theoretic Multi-Objective Bayesian Optimization with Continuous Approximations (iMOCA) selects input and function approximations to maximize information gain per unit cost.
result iMOCA significantly improves over existing single-fidelity methods in approximating the optimal Pareto set.
In this work, we introduce a new procedure for applying Restricted Boltzmann Machines (RBMs) to missing data inference tasks, based on linearization of the effective energy function governing the distribution of observations. We compare the performance of our proposed procedure with those obtained using existing recons…
New bandit algorithm works without realizability assumption.
problem Contextual bandit problems without realizability assumption.
method Computes a constrained regression problem in every epoch, ensuring similar regret guarantees as realizability-based algorithms.
result Ensures similar regret guarantees as realizability-based algorithms, up to a misspecification term.
The Sampled Gaussian Mechanism's noise level decreases with larger subsampling rates, improving privacy-utility trade-offs.
problem Improving privacy-utility trade-offs in differentially private stochastic optimization.
method Proof of a conjecture about the Sampled Gaussian Mechanism's noise level and subsampling rate relationship.
result A rigorous proof of the conjecture, completing the proof of Theorem 6.2 in the original paper.
Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance unbiased estimators of derivatives at any order. Our objective is compatible with arbit…
In this paper we study the stability and its trade-off with optimization error for stochastic gradient descent (SGD) algorithms in the pairwise learning setting. Pairwise learning refers to a learning task which involves a loss function depending on pairs of instances among which notable examples are bipartite ranking,…
Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on problems arising in continuous control, we propose a functional regularization appr…
Paper analyzes trade-offs in top-k classification accuracies and proposes a new loss function.
problem CE loss does not always optimize top-k prediction, especially with complex data.
method Introduces a novel top-k transition loss to improve top-k accuracy.
result Our loss function improves top-k accuracy, especially for k > 10.
The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly handled by algorithmic stability. The machine learning community has a rich his…
Study reveals decurve flows in graph propagation models.
problem Limitations of traditional graph analysis and propagation mechanisms.
method Introduces Generalized Propagation Neural Networks (GPNNs) and Continuous Unified Ricci Curvature (CURC).
result Observation of decurve flow during training of graph neural networks, revealing propagation dynamics.
New theory explains how overparametrized neural networks generalize well without bias-variance trade-off.
problem Overparametrized neural networks generalize well despite classical bias-variance trade-off.
method Nonasymptotic generalization theory for two-layer neural networks with ReLU activation, incorporating scaled variation regularization.
result Prediction bounds for all network widths reproduce the double descent phenomenon, and overparametrized models are nearly minimax optimal.
New insights into optimizing latent representations in hierarchical VAEs.
problem Optimizing latent representations in hierarchical VAEs for various applications.
method Identifying a general class of inference models and deriving theoretical bounds on performance.
result Guidance for practitioners on optimal regions in rate-space for different applications.
New expressive losses improve adversarial robustness without sacrificing accuracy.
problem Training networks for robustness at the expense of accuracy.
method Formalizing expressivity, using convex combinations of adversarial attacks and IBP bounds.
result Trivial expressive losses yield state-of-the-art results in various settings.
In this paper, several modifications are introduced to the functional approximation method iterLap to reduce the approximation error, including stopping rule adjustment, proposal of new residual function, starting point selection for numerical optimisation, scaling of Hessian matrix. Illustrative examples are also prov…
A new framework enables real-time task trade-off control.
problem Conflict between multiple related tasks in a fixed model capacity.
method Formulates MTL as a preference-conditioned multiobjective optimization problem; uses a hypernetwork-based neural network.
result A single model can handle different trade-off preferences among multiple tasks.
Asymptotic Theory and Phase Transitions for Variable Importance in Quantile Regression Forestsstat.ML
The paper develops asymptotic theory for QRF variable importance, revealing a bias-variance trade-off.
problem Challenges in statistical inference for QRF variable importance due to non-smoothness and bias-variance trade-off.
method Developed asymptotic theory using pinball loss and Knight's identity, uncovered phase transition phenomenon, derived asymptotic bias.
result Theoretical foundation for understanding QRF inference limitations in high-dimensional settings.
We consider an agent who is involved in a Markov decision process and receives a vector of outcomes every round. Her objective is to maximize a global concave reward function on the average vectorial outcome. The problem models applications such as multi-objective optimization, maximum entropy exploration, and constrai…
Greedy training of recursive partitioning estimators faces a computational barrier when the true function doesn't satisfy a specific property.
problem Computational inefficiency of greedy training for recursive partitioning estimators.
method Analysis of greedy training for sparse regression functions over binary features.
result Greedy training requires exponential samples when the true function doesn't satisfy a specific property (MSP), but only logarithmic samples when it does.
Paper explores robust regression methods and their bias-variance trade-off.
problem Understanding the trade-off between robust estimation and optimization methods.
method Examines traditional outlier-resistant robust estimation and robust optimization.
result Both methods follow converse strategies due to a bias-variance trade-off.
This paper studies trade-offs in private prediction methods.
problem Leakage of training data information in machine learning predictions.
method Private training and private prediction methods with trade-offs.
result Private training methods outperform private prediction methods in various settings.
Efficiently approximates fairness-accuracy trade-offs for diverse datasets.
problem Inherent trade-off between fairness and accuracy in machine learning models.
method You-Only-Train-Once (YOTO) framework for computationally efficient approximation.
result Robust methodology for auditing model fairness with statistical guarantees.
Deep Portfolio Theoryq-fin.PM
We construct a deep portfolio theory. By building on Markowitz's classic risk-return trade-off, we develop a self-contained four-step routine of encode, calibrate, validate and verify to formulate an automated and general portfolio selection process. At the heart of our algorithm are deep hierarchical compositions of p…
New algorithm reduces sample and communication complexities in federated Q-learning.
problem Optimal Q-function learning in federated Q-learning with limited communication.
method Introduced Fed-DVR-Q algorithm for order-optimal sample and communication complexities.
result Complete characterization of sample-communication complexity trade-off.
A new model for point processes without intensity function trade-offs.
problem Inefficiency and trade-offs in existing point process models.
method Point Set Diffusion, a diffusion-based latent variable model.
result Achieves state-of-the-art performance in point process generation.
The paper tackles mean-variance analysis in Bayesian optimization under uncertainty.
problem Optimizing decisions in uncertain environments considering trade-offs between average and variance of risk.
method Developed bounds for mean and variance risk measures in Gaussian Process models and proposed AL algorithms for multi-task, multi-objective, and constrained optimization scenarios.
result Proposed AL algorithms effectively address the mean-variance trade-off in uncertain optimization scenarios.
New insights into convergence and accuracy trade-offs in federated and meta-learning.
problem Understanding the trade-offs between convergence and accuracy in federated and meta-learning.
method Generalized local update methods, proving equivalence to first-order optimization on a surrogate loss.
result Novel convergence rates and insights into the importance of algorithmic choices in communication-limited settings.
New empirical process bounds reveal trade-off between dependence and complexity in nonparametric learning.
problem Understanding generalization in nonparametric learning with temporal dependencies.
method Developed bounds on expected supremum of empirical processes under -mixing assumptions.
result Achieved rates similar to i.i.d. setting under long-range dependence with complex function classes.
We empirically investigate the best trade-off between sparse and uniformly-weighted multiple kernel learning (MKL) using the elastic-net regularization on real and simulated datasets. We find that the best trade-off parameter depends not only on the sparsity of the true kernel-weight spectrum but also on the linear dep…
We describe convolutional networks using harmonic functions.
problem Understanding the function space and smoothness of convolutional networks.
method Using reproducing kernel Hilbert spaces and functional ANOVA decomposition.
result Convolutional networks can be decomposed into a sum of elementary functions.
PGEL learns embeddings to diversify protein motifs while maintaining biological function.
problem Generating diverse protein structures while preserving biological function.
method Embedding learning framework that enhances motif diversity in a diffusion model's frozen denoiser.
result PGEL achieves greater structural diversity, better designability, and improved self-consistency compared to partial diffusion.
Lossy Compression via Sparse Linear Regression: Computationally Efficient Encoding and Decodingcs.IT
We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The proposed encoding algorithm sequentially chooses columns of the design matrix to suc…
Proposes FACT, a diagnostic for understanding group fairness trade-offs.
problem Group fairness notions often conflict with each other, requiring a cost in model performance.
method Characterizes trade-offs via the fairness-confusion tensor and optimizes accuracy and fairness objectives.
result Demonstrates the use of FACT on synthetic and real datasets to understand accuracy-fairness trade-offs.