Near-Exponential Convergence Rates for kNN Classification
problem Convergence rates for kNN classification
method Introducing Boltzmann margin
result First near-exponential convergence rates for kNN classification
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48 results for “margin analysis”
Random projections have been applied in many machine learning algorithms. However, whether margin is preserved after random projection is non-trivial and not well studied. In this paper we analyse margin distortion after random projection, and give the conditions of margin preservation for binary classification problem…
Improved Sample Complexities for Deep Networks and Robust Classification via an All-Layer Margincs.LG
For linear classifiers, the relationship between (normalized) output margin and generalization is captured in a clear and simple bound -- a large output margin implies good generalization. Unfortunately, for deep models, this relationship is less clear: existing analyses of the output margin give complicated bounds whi…
We introduce a useful tool for analyzing boosting algorithms called the ``smooth margin function,'' a differentiable approximation of the usual margin for boosting algorithms. We present two boosting algorithms based on this smooth margin, ``coordinate ascent boosting'' and ``approximate coordinate ascent boosting,'' w…
This paper studies binary classification problem associated with a family of loss functions called large-margin unified machines (LUM), which offers a natural bridge between distribution-based likelihood approaches and margin-based approaches. It also can overcome the so-called data piling issue of support vector machi…
Paper analyzes GMM for separable data with various parameter structures.
problem Classifying separable data with logistic models and their generalizations.
method Introduces and analyzes Generalized Margin Maximizer (GMM) for logistic models with specific parameter structures.
result GMM outperforms max-margin classifiers in various parameter settings and structures.
Study shows exponential error reduction in multiclass classification without bias-variance trade-off.
problem Multiclass classification with margin conditions.
method Analysis of classification error under hard-margin conditions.
result Exponential decrease in classification error without bias-variance trade-off.
Study examines liquidation, leverage, and optimal margin requirements in Bitcoin futures markets.
problem Understanding and optimizing margin requirements in Bitcoin futures markets.
method Empirical analysis using generalized extreme value theory and BitMEX data.
result Margin requirements need to be significantly higher to reduce daily margin calls.
This paper shows that the implicit bias of gradient descent on linearly separable data is exactly characterized by the optimal solution of a dual optimization problem given by a smoothed margin, even for general losses. This is in contrast to prior results, which are often tailored to exponentially-tailed losses. For t…
Unified binary and multiclass margin-based classification methods.
problem No consensus on multiclass loss functions analogous to binary margin loss.
method Showed multiclass loss functions can be expressed in relative margin form.
result Extended classification-calibration result to multiclass.
This paper is devoted to the quantification and analysis of marginal risk contribution of a given single financial institution i to the risk of a financial system s. Our work expands on the CoVaR concept proposed by Adrian and Brunnermeier as a tool for the measurement of marginal systemic risk contribution. We first g…
Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal. In the probabilistic interpretation of low-rank PCA, the data has a normal multiv…
Both in practice and in the academic literature, models for setting margin requirements in futures markets classically use daily closing price changes. However, as well documented by research on high-frequency data, financial markets have recently shown high intraday volatility, which could bring more risk than expecte…
In critical decision-making scenarios, optimizing accuracy can lead to a biased classifier, hence past work recommends enforcing group-based fairness metrics in addition to maximizing accuracy. However, doing so exposes the classifier to another kind of bias called infra-marginality. This refers to individual-level bia…
Paper reinterprets marginal productivity theory using vectorial products, challenging traditional ethical interpretations.
problem Challenges traditional ethical interpretations of marginal productivity theory.
method Formulates marginal productivity theory using vectorial marginal products, contrasting with traditional scalar approach.
result Vectorial marginal products conflict with traditional distributive shares picture of property.
Support vector regression (SVR) is one of the most popular machine learning algorithms aiming to generate the optimal regression curve through maximizing the minimal margin of selected training samples, i.e., support vectors. Recent researchers reveal that maximizing the margin distribution of whole training dataset ra…
Solves a 60-year-old question on agreement measures in statistics.
problem The challenge of measuring agreement between two raters or measures.
method Developed a new algorithm to minimize diagonals in contingency tables, formulated the minimum feasible agreement, and studied the lower limit of maximum feasible agreement.
result Formulated the lower limit of Cohen's kappa and two statistics for agreement analysis.
DAIS improves AIS for differentiable marginal likelihood estimation.
problem Differentiable marginal likelihood estimation for complex models.
method Proposes Differentiable Annealed Importance Sampling (DAIS) to make AIS differentiable.
result DAIS achieves convergence and consistency in Bayesian linear regression.
Interpretability has emerged as a crucial aspect of building trust in machine learning systems, aimed at providing insights into the working of complex neural networks that are otherwise opaque to a user. There are a plethora of existing solutions addressing various aspects of interpretability ranging from identifying …
Identifies interpretable generative model for multivariate data.
problem Black-box architectures of deep generative models are often unidentified and difficult to interpret.
method Introduces Deep Discrete Encoder (DDE) Copula, a hierarchical binary latent variable model inside a copula framework.
result Establishes conditions for identification of DDE copula parameters and proves posterior consistency.
Large scale analysis of generalization error in learning using margin based classification methodsstat.ML
Derives asymptotic generalization error for large-margin classifiers.
problem Understanding the generalization error of large-margin classifiers.
method Statistical physics replica method for deriving asymptotic expression.
result Establishes phase transition boundary for class separability.
This work analyzes the maximum-margin bias in quasi-homogeneous neural networks.
problem Analyzing the maximum-margin bias in quasi-homogeneous neural networks.
method Geometric analysis of gradient dynamics for quasi-homogeneous models.
result Gradient flow implicitly favors a subset of parameters, leading to asymmetric norm minimization.
The paper analyzes the maximum margin algorithm's performance on noisy data.
problem Analyzing the performance of maximum margin algorithm on noisy data.
method Finite-sample analysis of maximum margin algorithm applied to noisy data.
result The maximum margin algorithm can achieve nearly optimal population risk with sufficient over-parameterization.
We consider the problem of discriminative factor analysis for data that are in general non-Gaussian. A Bayesian model based on the ranks of the data is proposed. We first introduce a new {\em max-margin} version of the rank-likelihood. A discriminative factor model is then developed, integrating the max-margin rank-lik…
Study on neuron dynamics for XOR classification with zero-margin.
problem Understanding neural network training dynamics in zero-margin classification problems.
method Analysis of Gaussian XOR problem, focusing on neuron block dynamics and generalization without margin assumptions.
result Neurons cluster into four directions and block-level signals evolve coherently, essential for reliable prediction in the Gaussian setting.
One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter gamma. From a practical point of view, the theoretical analysis of generalization performance contribut…
Gradient descent and SGD achieve low test error in specific network weight regimes.
problem Optimizing two-layer ReLU networks with standard initialization.
method Gradient flow and stochastic gradient descent, analyzing margins and weight norms.
result Gradient descent and SGD can achieve globally maximal margins under certain constraints.
In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using cross-validation on held-out data, either through -fold partitioning or leave-$p…
Existence proved for -Bass martingales with specific marginals.
problem Constructing martingales with prescribed marginals close to a reference measure.
method Geometric analysis of parametrized convex polygonal chains.
result Existence and uniqueness of -Bass martingales with finitely supported initial marginals.
Proposes a method to construct risk-neutral marginals from arbitrage-free option prices.
problem Lack of risk-neutral marginals that are free of arbitrage and easy to use.
method Explicit construction of risk-neutral marginals from discrete arbitrage-free option prices.
result Explicit construction guarantees risk-neutral marginals free of butterfly and calendar arbitrage.
New margin-based regularization and selective sampling improve deep neural network performance.
problem Improving deep neural network performance on various classification tasks.
method Multi-margin regularization (MMR) and minimal margin score (MMS) for selective sampling.
result Improved results on multiple classification tasks across domains.
Paper resolves conflicting Shapley value approaches by showing conditional is unsound and marginal is preferred.
problem Conflicting results from conditional and marginal Shapley value approaches when features are correlated.
method Uses causal arguments to show differences arise from assumptions about missing causal information.
result Marginal approach is preferred over conditional due to causal soundness.
Standard methods for anomaly detection assume that all features are observed at both learning time and prediction time. Such methods cannot process data containing missing values. This paper studies five strategies for handling missing values in test queries: (a) mean imputation, (b) MAP imputation, (c) reduction (redu…
Improved Gaussian process regression with tighter log marginal likelihood bounds.
problem Improving predictive performance in Gaussian process regression models.
method Lower bound on log marginal likelihood using conjugate gradients.
result Improved predictive performance compared to other conjugate gradient based approaches.
Tropical SVM tackles phylogenomics by classifying multi-locus data.
problem Classifying multi-locus data sets for phylogenetic analysis.
method Proposes tropical support vector machines (SVMs) for phylogenomics, formulated as linear programming problems.
result Developed methods for hard and soft margin tropical SVMs, proving necessary and sufficient conditions for separation.
Improved MUSE boosts performance and reduces error in Bayesian inference.
problem Hierarchical Bayesian inference problems
method Implicit differentiation applied to MUSE algorithm
result Significant speedup and improved accuracy compared to Hamiltonian Monte Carlo
Link prediction is a fundamental task in statistical network analysis. Recent advances have been made on learning flexible nonparametric Bayesian latent feature models for link prediction. In this paper, we present a max-margin learning method for such nonparametric latent feature relational models. Our approach attemp…
In order to face the expected increasing demand of energy crops without creating conflicts of land occupation sustainability, farmers need to find reliable alternatives in marginal agricultural areas where the production of food hardly ever is economically and environmentally sustainable. The purpose of this work was t…
We solve the -marginal Skorokhod embedding problem for a continuous local martingale and a sequence of probability measures which are in convex order and satisfy an additional technical assumption. Our construction is explicit and is a multiple marginal generalisation of the Azema and Yor (1979) soluti…
Machine learning predicts CO2 emissions in power grids, reducing uncertainty.
problem Forecasting CO2 emission intensities in power grids.
method Developed a machine learning algorithm using LASSO, feature selection, and Softmax weighted average.
result Marginal emissions are independent of DK2 zone conditions, suggesting external generators.
This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk to the case where collateral is included, with possible re-hypotecation. We analyze how the payout of claims is modified when collateral margining is included in agreement with current ISDA documentation. We then specialize…
The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networkscs.LG
SGD converges to critical points of normalized margin in late-stage training for homogeneous neural networks.
problem Analyzing the implicit bias of SGD on homogeneous neural networks.
method Interpreting SGD dynamics as an Euler-like discretization of a conservative field flow associated with the normalized classification margin.
result Normalized SGD iterates converge to the set of critical points of the normalized margin at late-stage training.
Margin-based classifiers have been popular in both machine learning and statistics for classification problems. Since a large number of classifiers are available, one natural question is which type of classifiers should be used given a particular classification task. We answer this question by investigating the asympto…
Bayesian models use hyperparameters to indirectly assign priors, and this work shows how these priors can be derived from maximum entropy principles.
problem Understanding the assumptions and dependencies in Bayesian hierarchical models.
method Demonstrates how canonical distributions and maximum entropy principles can be used to derive marginal priors in hierarchical models.
result Marginal priors in hierarchical models derived from maximum entropy principles have different constraints compared to the original priors.
New algorithm improves latent variable model estimation.
problem Estimating parameters in latent variable models.
method Jarzynski-adjusted Langevin algorithm (JALA) for SMC methods.
result JALA-EM provides maximum marginal likelihood estimate.
We analyze the semi-hard triplet loss using Edgeworth expansion for better understanding of its behavior.
problem Understanding the behavior of the semi-hard triplet loss function.
method Developed a higher-order asymptotic analysis using the Edgeworth expansion.
result Derived explicit Edgeworth expansions revealing first-order corrections in terms of the third cumulant.
A deep BSDE approach tackles multi-layered xVA calculations for portfolio valuation.
problem Computational intractability in nested simulations for multi-layered xVA calculations.
method Iterative deep BSDE approach, change-of-measure method, quantile regression for margin computation.
result Reduces computational demands and successfully scales to high-dimensional portfolios.
This paper works out fair values of stock loan model with automatic termination clause, cap and margin. This stock loan is treated as a generalized perpetual American option with possibly negative interest rate and some constraints. Since it helps a bank to control the risk, the banks charge less service fees compared …