Theoretical analysis of cross-entropy loss functions and their robustness.
problem Guarantees for using cross-entropy as a surrogate loss function.
method Theoretical analysis of a broad family of loss functions, including cross-entropy.
result First H-consistency bounds for comp-sum losses and smooth adversarial comp-sum losses. A new method for forming learning objectives using the sum of ranked range.
problem Forming learning objectives from aggregated values.
method Sum of ranked range (SoRR) minimization with DCA.
result The proposed method effectively forms learning objectives and is applicable to binary and multi-label/multi-class classification.
We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the su…
Introduces SoRR for aggregating losses in supervised learning.
problem Aggregating individual losses into a single output for machine learning models.
method Sum of ranked range (SoRR) minimization using DCA.
result Demonstrates effectiveness of AoRR and TKML in improving robustness of multi-label learning.
Improved GAN training stability through tunable classification losses.
problem Training instabilities in GANs.
method Reformulated GAN value function using class probability estimation (CPE) losses, defined (αD,αG)-GANs. result Tuning (αD,αG) can alleviate training instabilities. Study on H-consistency bounds for machine learning surrogates.
problem Estimating target loss error relative to surrogate loss error in machine learning.
method Developed H-consistency bounds for various surrogates and loss functions. result Stronger guarantees than existing methods, offering distribution-dependent and -independent bounds.
Ranking is a key aspect of many applications, such as information retrieval, question answering, ad placement and recommender systems. Learning to rank has the goal of estimating a ranking model automatically from training data. In practical settings, the task often reduces to estimating a rank functional of an object …
Study on top-k classification with new loss functions and algorithms.
problem Improving multi-class classification accuracy and cardinality trade-off.
method Introducing cardinality-aware loss functions and deriving their consistency bounds.
result New cardinality-aware algorithms for top-k classification. Unified surrogate loss framework for multi-label learning with strong consistency guarantees.
problem Improving consistency and accounting for label correlations in multi-label learning.
method Introducing multi-label logistic loss and extending it to comprehensive multi-label comp-sum losses, proving strong consistency guarantees for any multi-label loss.
result Unified surrogate loss framework benefiting from strong consistency guarantees for any multi-label loss.
Paper studies multiclass classifiers from binary classifiers, proving methods and demonstrating advantages.
problem Constructing efficient multiclass classifiers from binary ones.
method Two methods: one vs. all and hierarchical classification, with a new leverage-hierarchical method introduced.
result Proves upper bounds and exact formulas for multiclass regret in terms of binary regrets.
New method for sequential probability assignment reduces regret using contextual Shtarkov sums.
problem Minimizing regret in sequential probability assignment with arbitrary hypothesis classes.
method Introducing contextual Shtarkov sum and contextual Normalized Maximum Likelihood (cNML) algorithm.
result The contextual Shtarkov sum characterizes minimax regret and provides a minimax optimal strategy.
Improves deep learning models by blending gradients from training loss and auxiliary objective.
problem Minimizing a single training loss while encouraging desirable model properties.
method Solves a bilevel optimization problem by combining training loss gradients and orthogonal projections of auxiliary gradients.
result Bloop method leads to better performance than other gradient surgery methods without EMA.
Paper establishes a universal growth rate for smooth surrogate losses in classification.
problem Analyzing growth rates of consistency bounds for various surrogate losses.
method Proves square-root growth rate for smooth margin-based losses; extends to multi-class classification.
result Demonstrates a universal square-root growth rate for smooth comp-sum and constrained losses.
New algorithm predicts tensor entries faster than best rank-r tensor.
problem Agnostic tensor completion with unknown rank.
method Sum-of-squares relaxation of tensor nuclear norm.
result Prediction error rate of O(r2d3/2/n), improving over matrix completion. Here we present an application of two maxentropic procedures to determine the probability density distribution of compound sums of random variables, using only a finite number of empirically determined fractional moments. The two methods are the Standard method of Maximum Entropy (SME), and the method of Maximum Entrop…
Sum-product networks (SPNs) represent an emerging class of neural networks with clear probabilistic semantics and superior inference speed over graphical models. This work reveals a strikingly intimate connection between SPNs and tensor networks, thus leading to a highly efficient representation that we call tensor SPN…
Independent component analysis (ICA) is a widespread data exploration technique, where observed signals are modeled as linear mixtures of independent components. From a machine learning point of view, it amounts to a matrix factorization problem with a statistical independence criterion. Infomax is one of the most used…
Proposes a simple framework to balance task difficulty in multi-task learning.
problem Varying difficulty levels among different tasks in multi-task learning.
method Introduces a Balanced Multi-Task Learning (BMTL) framework that transforms training losses to balance task difficulty.
result Empirical studies show state-of-the-art performance of the proposed BMTL framework.
In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the expected loss and not on finite-sum minimization, which is typically a much harder p…
A perturbative approach is used to derive approximations of arbitrary order to estimate high percentiles of sums of positive independent random variables that exhibit heavy tails. Closed-form expressions for the successive approximations are obtained both when the number of terms in the sum is deterministic and when it…
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.
L2S unifies SARAH for sum of losses with improved convergence.
problem Finding accurate solutions to problems with multiple loss functions.
method Loop-less SARAH (L2S) for sum of losses, with improved complexity and step sizes.
result L2S achieves better generalization properties and faster convergence in neural networks.
Proposes squentropy loss for improved classification accuracy and model calibration.
problem Theoretical and empirical evidence for cross-entropy loss is lacking.
method Introduces squentropy loss as the sum of cross-entropy and average square loss over incorrect classes.
result Squentropy loss outperforms cross-entropy and rescaled square losses in classification accuracy and model calibration.
This paper mixes constant sum and constant product market makers to improve their features.
problem Improving the balance between stable exchange rates and liquidity in automated market makers.
method Mixing and designing new methods for AMMs with specific features.
result Demonstrates new tools for creating markets with desired characteristics.
We present a new machine learning approach to estimate personalized treatment effects in the classical potential outcomes framework with binary outcomes. To overcome the problem that both treatment and control outcomes for the same unit are required for supervised learning, we propose surrogate loss functions that inco…
This paper explains how low-precision arithmetic causes loss spikes in deep learning models.
problem Loss spikes during long-term training of deep neural networks.
method Analyzes the impact of floating-point precision limits on gradient updates and feature means.
result Numerical Feature Inflation (NFI) explains loss spikes and rapid parameter norm growth.
In this paper we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process, by using the Malliavin calculus. In analogy with the celebrated Black-Scholes formula, we aim at expressing the expected cash flow in terms of a building block. The former is r…
A new SGD variant chooses the sample with lowest loss to make the model more robust to outliers.
problem Outliers can skew the parameters of machine learning models trained via SGD.
method Choose a set of k samples, then select the one with the smallest current loss for update.
result The new method makes SGD more robust for ML problems that are sums of convex losses.
New framework guarantees convergence of multi-step MAML.
problem Convergence of multi-step MAML in nonconvex settings.
method Developed a theoretical framework for two types of MAML objective functions.
result Guaranteed convergence rate and computational complexity for multi-step MAML.
Study improves top-k set prediction with low cardinality.
problem Improving top-k set prediction accuracy with low cardinality.
method Introduces new target loss function and surrogate losses.
result Demonstrates effectiveness of cardinality-aware algorithms.
New method preserves privacy by aggregating feature-vectors with weighted sums, ensuring label differential privacy.
problem Ensuring privacy in training data aggregation for sensitive labels.
method Learning from bag aggregates (LBA) with weighted Gaussian sums, preserving label differential privacy (label-DP).
result Weighted LBA using iid Gaussian weights with m randomly sampled disjoint k-sized bags provides (ε,δ)-label-DP. Kjolstad et. al. proposed a tensor algebra compiler. It takes expressions that define a tensor element-wise, such as fij(a,b,c,d)=exp[−∑k=04((aik+bjk)2cii+di+k3)], and generates the corresponding compute kernel code. For machine learning, especially deep learni…
Dynamic regret minimization is shown equivalent to static regret minimization for linear losses.
problem Dynamic regret minimization in online convex optimization.
method Equivalence between dynamic and static regret minimization for linear losses.
result Dynamic regret minimization is equivalent to static regret minimization for linear losses.
Delaytron learns multi-class classifiers with delayed feedbacks, achieving efficient regret bounds.
problem Learning multi-class classifiers with delayed bandit feedbacks where delays are unknown.
method Online algorithm Delaytron with adaptive learning for unknown delays.
result Achieves efficient regret bounds for various loss scenarios.
Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational bottleneck being inference that is intractable. Tractable learning is a powerful new p…
In this paper we consider online mirror descent (OMD) algorithms, a class of scalable online learning algorithms exploiting data geometric structures through mirror maps. Necessary and sufficient conditions are presented in terms of the step size sequence {ηt}t for the convergence of an OMD algorithm with respe…
Simplifies risk minimization combining mean and standard deviation.
problem Minimizing mean and standard deviation under heavy-tailed losses.
method Adapting robust mean estimation technique to include standard deviation.
result Simple approach performs as well or better than alternative risk criteria.
New optimization method improves AUC for binary classification and changepoint detection.
problem Non-convex AUC and sub-optimal points in ROC curves.
method AUM (Area Under Min(FP, FN)) surrogate loss function based on sorting and summing ROC curve points.
result AUM minimization learning algorithm improves AUC and speeds up compared to previous methods.
Deep learning optimizes constellation for two-way relaying networks, boosting sum rate.
problem Optimizing constellation for better performance in two-way relaying networks.
method Deep neural networks (DNNs) trained to minimize cross entropy loss for direct constellation optimization.
result Significant performance gain in achievable sum rate compared to conventional relaying schemes.
In this paper we prove local analytic hypoellipticity for a degenerate sum of squares of complex vector fields generalizing those of Kohn in "Hypoellipticity and Loss of Derivatives". Kohn's article is to appear in the Annals of Mathematics with an appendix by Derridj and Tartakoff proving local analyticity in that cas…
Proposes a new training algorithm for zero-sum games to avoid convergence issues.
problem Gradient-based training leads to weak convergence and cyclic dynamics in zero-sum architectures.
method Follow the perturbed leader algorithm with neural mediating agent.
result Guarantees convergence to mixed Nash equilibrium without cyclic behaviors.
We prove that the empirical risk of most well-known loss functions factors into a linear term aggregating all labels with a term that is label free, and can further be expressed by sums of the loss. This holds true even for non-smooth, non-convex losses and in any RKHS. The first term is a (kernel) mean operator --the …
Develops a new theory of loss functions for statistical machine learning.
problem Evaluation of solutions in binary and multiclass classification problems.
method Defines loss functions as subgradients of support functions of convex sets, enabling a calculus of losses.
result Provides a novel perspective on losses and develops a calculus that interpolates between different losses.
DESTRESS optimizes decentralized nonconvex optimization with optimal IFO complexity and efficient communication.
problem Decentralized nonconvex finite-sum optimization in multi-agent systems.
method DESTRESS uses stochastic recursive gradient updates, gradient tracking, and careful hyper-parameter choices to achieve optimal IFO complexity with efficient communication.
result DESTRESS matches the optimal IFO complexity of centralized algorithms while maintaining communication efficiency.
We propose a simple discrete time semi-supervised graph embedding approach to link prediction in dynamic networks. The learned embedding reflects information from both the temporal and cross-sectional network structures, which is performed by defining the loss function as a weighted sum of the supervised loss from past…
This paper improves SAM by reformulating it as a bilevel optimization problem.
problem Improving Sharpness-Aware Minimization (SAM) for better performance.
method Reformulate SAM as a bilevel optimization problem using a 0-1 loss surrogate.
result BiSAM consistently results in improved performance compared to SAM and its variants.
This work tackles Bayesian neural networks by addressing loss landscape symmetries.
problem Understanding and optimizing the loss landscape of Bayesian neural networks.
method The approach involves extending marginalized loss barrier formalism to BNNs, proposing a matching algorithm to search for linearly connected solutions using permutation matrices and combinatorial optimization.
result Nearly zero marginalized loss barriers for linearly connected solutions were found.
ProxSPS improves on SPS for regularization tasks, offering better stability and performance.
problem Handling regularization terms in adaptive step size schemes for stochastic gradient descent.
method Developed a proximal variant of the stochastic Polyak step size (SPS) scheme.
result ProxSPS is easier to tune and more stable with regularization, and performs well in image classification tasks.