Paper explores connections between loss functions and consistency in binary classification and regression.
problem Consistency in binary classification and regression applications.
method Characterization of conformable loss functions and derivation of a new Huber-type loss function.
result Margin-based loss functions are equivalent to loss functions of squared standardized logistic regression residuals.
A new method for exponentially weighted moving models using approximations.
problem Efficiently updating moving averages for time series data.
method Approximates EWMM using a fixed window and quadratic term, solving non-growing problems.
result Approximation produces estimates similar to exact EWMM.
Gradient descent implicitly follows regularization for general losses.
problem The implicit bias of gradient descent methods in machine learning.
method Empirical risk minimization over linear predictors with arbitrary convex, strictly decreasing losses.
result Gradient descent and regularization paths converge to the same direction for non-attained risks.
AUC (area under ROC curve) is an important evaluation criterion, which has been popularly used in many learning tasks such as class-imbalance learning, cost-sensitive learning, learning to rank, etc. Many learning approaches try to optimize AUC, while owing to the non-convexity and discontinuousness of AUC, almost all …
Exponential testing error reduction with stochastic gradient methods under low-noise conditions.
problem Binary classification with positive definite kernels and square loss.
method Stochastic gradient methods under low-noise conditions.
result Testing error converges exponentially fast, while testing loss converges slowly.
Paper proposes a new e-exponentiated transformation to make convex loss functions more robust to outliers.
problem Making convex loss functions robust to outliers in the presence of label noise.
method Introduces a novel e-exponentiated transformation for loss functions and proves its effectiveness through theoretical and empirical analysis. result The transformed loss function achieves tighter generalization error bounds and higher accuracy in noisy datasets.
Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.
problem Lasso's sensitivity to outliers and heavy-tailed noise in high-dimensional statistics.
method Integrates an exponential-type loss function into the Lasso framework.
result Achieves strong statistical convergence rates robust to heavy-tailed contamination.
Proposes a new classification model using extended exponential functions.
problem Improving classification accuracy in binary linear classification problems.
method Developed a Bregman-Tweedie classification model based on extended exponential functions.
result The H-Bregman and L-Bregman sub-models outperform traditional methods in ranking and classification accuracy.
New aggregation strategy handles unbounded losses with regret bounds.
problem Online optimization with unbounded loss functions.
method Follow The Regularized Leader (FTRL) with φ-divergence.
result Worst regret bound for unbounded losses with alternative divergences.
Adapts exponential weights algorithm for kernel losses in online learning.
problem Online learning with kernel losses.
method Adapts exponential weights algorithm for kernel losses.
result Sharp bounds on regret for different kernel eigendecay conditions.
Paper compares VaR from aggregated and single loss distributions in credit risk.
problem Estimating VaR in credit risk portfolios with varying severities.
method Uses Monte Carlo simulation with Gamma and truncated exponential distributions.
result Truncated exponential distribution yields VaR closer to aggregated loss approach.
We study online learning under logarithmic loss with regular parametric models. Hedayati and Bartlett (2012b) showed that a Bayesian prediction strategy with Jeffreys prior and sequential normalized maximum likelihood (SNML) coincide and are optimal if and only if the latter is exchangeable, and if and only if the opti…
Study on loss probabilities for diversified financial systems with light-tailed claims.
problem Analyzing risks in systems of diversified financial agents with light-tailed claims.
method Assuming exponentially distributed claims, we derive conditional loss distributions and compare with heavy-tailed claims.
result Conditional loss distributions reveal different risk profiles for agents and systems compared to heavy-tailed claims.
The AdaBoost algorithm was designed to combine many "weak" hypotheses that perform slightly better than random guessing into a "strong" hypothesis that has very low error. We study the rate at which AdaBoost iteratively converges to the minimum of the "exponential loss." Unlike previous work, our proofs do not require …
Boosting with tempered exponential measures improves AdaBoost's convergence rate.
problem Improving the convergence rate of AdaBoost.
method Introducing tempered exponential measures (TEMs) to generalize AdaBoost's approach.
result t-AdaBoost achieves an improved convergence rate compared to AdaBoost, especially for t∈[0,1). We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an average of the past examples. After receiving an example the algorithm incurs a loss which is the negative log-likelihood…
We consider the problem of learning a forest of nonlinear decision rules with general loss functions. The standard methods employ boosted decision trees such as Adaboost for exponential loss and Friedman's gradient boosting for general loss. In contrast to these traditional boosting algorithms that treat a tree learner…
The L1 loss landscape of neural nets near local minima behaves differently, revealing exponential decay and increased vertex density.
problem Understanding the L1 loss landscape of neural nets near local minima.
method Iterative minimization of the loss function on adjacent vertices of the Deep ReLU Simplex algorithm.
result Exponential decay of loss levels and increased vertex density around local minima.
SPLBoost improves robustness of AdaBoost by incorporating self-paced learning.
problem AdaBoost's sensitivity to random noise/outliers.
method Integrating self-paced learning into Boosting framework.
result SPLBoost achieves improved robustness compared to traditional Boosting algorithms.
We consider the problem of rank loss minimization in the setting of multilabel classification, which is usually tackled by means of convex surrogate losses defined on pairs of labels. Very recently, this approach was put into question by a negative result showing that commonly used pairwise surrogate losses, such as ex…
Exponential Weights simplifies many online learning methods.
problem Developing and understanding online learning algorithms.
method Using Exponential Weights as a foundational approach to derive various online learning methods.
result Many online learning methods can be seen as special cases of Exponential Weights.
Logitron combines Perceptron and logistic loss for improved classification.
problem Non-convex and non-smooth zero-one loss function in classification models.
method Introduces a Perceptron-augmented convex classification framework with an extended logistic loss function.
result Hinge-Logitron outperforms logistic regression and SVM in classification accuracy.
We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transactions is used to obtain a tractable model. A general expansion theory is de…
This work extends implicit bias analysis to multiclass classification using a new loss framework.
problem The implicit bias of gradient descent on multiclass data without explicit regularization.
method Employing the PERM framework to introduce a multiclass extension of the exponential tail property.
result Extended implicit bias result to multiclass classification using a new loss framework.
Novel loss functions improve decision tree learning from noisy data.
problem Training decision trees with noisy labels.
method Introducing distribution losses and a new negative exponential loss.
result The negative exponential loss leads to efficient and robust decision tree learning.
The study offers new theoretical insights into structured prediction with convex loss minimization.
problem The challenge of structured prediction with efficient convex surrogate loss minimization.
method Constructing a convex surrogate loss and proving tight bounds on the calibration function.
result Formalizes the intuition that some task losses make learning harder than others, and that 0-1 loss is ill-suited for general structured prediction.
Researchers improve NCE by addressing its flat loss landscape issues.
problem NCE's poor performance due to an ill-behaved loss landscape.
method Introduced eNCE with an exponential loss and normalized gradient descent.
result Proven that landscape issues arise from inappropriate noise distribution.
Paper studies convergence rates from surrogate risk minimizers to Bayes optimal classifier.
problem Analyzing the convergence rates of surrogate risk minimizers to the Bayes optimal classifier.
method Introducing consistency intensity to characterize surrogate loss functions and using it to derive convergence rates.
result Empirical surrogate risk minimizers converge faster to the Bayes optimal classifier under certain conditions.
A fast method for training linear classifiers maximizes margins.
problem Training linear classifiers with maximum margins.
method Momentum-based gradient method derived from convex dual with Nesterov acceleration.
result Exponentially faster convergence rate compared to standard methods.
The paper extends mixability theory to function-valued forecasts, proving various loss functions are mixable.
problem Efficient aggregation of functional and probabilistic forecasts in online prediction games.
method Adapting mixable and exponentially concave loss functions to function-valued forecasts.
result Various loss functions used for probabilistic forecasting are mixable (exp-concave).
AEW estimator achieves optimal risk in expectation for large enough temperatures.
problem Understanding minimax-rate optimality of AEW estimator in model selection aggregation.
method Analyzing AEW estimator with exponential weights for squared loss under random design.
result AEW achieves excess risk Tlog(M)/(n+1) in expectation for large enough temperatures. New bound shows variational algorithms may struggle with barren plateaus.
problem Barren plateaus in quantum loss landscapes.
method General bound on loss variance and gradient decay.
result Exponential decay of gradients in subregions of barren plateaus.
Gradient EM converges exponentially to optimal solution in agnostic mixtures.
problem Fitting k parametric functions to given data points without a generative model. method Gradient EM algorithm for agnostic mixtures of arbitrary parametric functions.
result Gradient EM converges exponentially to population loss minimizers with high probability.
Unified framework approximates gradient descent's implicit bias in high dimensions.
problem Understanding gradient descent's behavior in overparameterized settings with convex losses.
method Unified framework for convex losses, including sensitivity analysis.
result Approximation of minimum-norm interpolation in high dimensions.
New algorithm reduces online logistic regression regret without exponential constant.
problem Improper learning in online logistic regression with logarithmic regret.
method Regularized empirical risk minimization with surrogate losses.
result Regret scaling as O(B log(Bn)) with low computational complexity.
Fast classification for sparse models, even with correlated features.
problem Sparse classification with many correlated features.
method Linear and quadratic surrogate cuts, priority queue, and analytical solution for exponential loss.
result 2 to 5 times faster than previous approaches, interpretable models with comparable accuracy.
A new risk distribution model reduces inflated risk capital calculations.
problem Inflated risk capital calculations due to very large losses from conduct risk.
method A novel distribution with an exponential of a fourth power, estimated using symbolic computation and numeric calculations.
result The proposed exponential density produces a more accurate risk capital calculation without loss frequency and severity limits.
Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum likelihood estimates (MLE) based on the data subsets, and then combines the local MLEs t…
Proposes an exponentially increasing step-size for faster parameter estimation in statistical models.
problem Slow convergence of gradient descent in locally convex loss functions.
method Exponentially increasing step-size in gradient descent algorithm.
result Converges linearly to optimal solution under homogeneous assumptions.
Paper proposes IE loss for deep metric learning improving CNN performance.
problem Improving deep learning models' performance in classification tasks.
method IE loss method to force distance between samples and class centers.
result IE loss leads to great improvements on various datasets.
Paper shows SVM can achieve super fast convergence rates.
problem Understanding fast convergence rates for SVM.
method Presented a simple mechanism to obtain fast convergence rates for SVM.
result SVM can exhibit exponential convergence rates without hard Tsybakov margin condition.
Online isotonic regression achieves optimal regret with a covering net approach.
problem Online isotonic regression with adversarial label placement.
method Exponential Weights algorithm over a covering net of isotonic functions.
result Exponential Weights achieves O(T1/3log2/3(T)) regret, matching a lower bound. Catapult phase in neural nets shows exponential loss growth before quick decrease.
problem Understanding phase transitions in neural networks during training.
method Analyzing weight norm and loss behavior for super-critical learning rates.
result Proven existence of catapult phase in quadratic models and two-layer nets.
This paper shows faster convergence rates for stochastic gradient descent in binary classification.
problem Achieving faster convergence rates for stochastic gradient descent in binary classification.
method Stochastic gradient descent and averaging variant, focusing on exponential convergence rates under strong low-noise conditions.
result Exponential convergence of the expected classification error in the final phase of stochastic gradient descent and averaged stochastic gradient descent for differentiable convex loss functions.
Proposes a new loss function for robust learning.
problem Creating a robust loss function for machine learning.
method Extended pseudo Huber loss with log-exp transform and logistic function.
result Linear convergence algorithm for minimizer finding.
A framework connects VAEs to GLMs for better model initialization and performance.
problem Understanding and optimizing loss function critical points in VAEs.
method Introducing a theoretical framework based on GLM and EDFs.
result Maximum likelihood initialization improves VAE performance.
Develops hedging algorithm for online expert weight allocation with delayed feedback.
problem Adaptive hedging strategies for online expert weight allocation with delayed feedback.
method General Hedging algorithm G based on exponential reweighing of experts' losses. result Proves adversarial loss bounds for the General Hedging algorithm G in the delayed feedback setting. A new method for robust training under label noise using weighted gradient descent.
problem Overfitting to noisy examples in machine learning.
method Exponentiated gradient reweighting for flexible handling of noisy data.
result Improved generalization in noisy classification and PCA problems.