New method improves GANs by estimating density ratios in feature space with SP loss.
problem Filtering out unrealistic images from GANs trained with suboptimal discriminators.
method Develops DRE-F-SP method based on Softplus loss for density ratio estimation in feature space, and proposes three subsampling methods.
result Empirically shows substantial improvement over existing methods on synthetic and CIFAR-10 datasets.
A new method lifts training of input-convex neural networks to avoid dead weights and plateaued loss.
problem Training input-convex neural networks with non-negative weights.
method Introduces a hypernetwork that emits non-negative weights from a summary of the input batch, adding stochasticity to soften the loss landscape.
result The lift method achieves lower test loss than projected gradient descent and direct softplus reparametrization.
To model categorical response variables given their covariates, we propose a permuted and augmented stick-breaking (paSB) construction that one-to-one maps the observed categories to randomly permuted latent sticks. This new construction transforms multinomial regression into regression analysis of stick-specific binar…
To construct flexible nonlinear predictive distributions, the paper introduces a family of softplus function based regression models that convolve, stack, or combine both operations by convolving countably infinite stacked gamma distributions, whose scales depend on the covariates. Generalizing logistic regression that…
SGD converges globally to logistic loss minima for two-layer nets.
problem Global convergence of SGD for logistic loss on two-layer neural nets.
method Demonstrates existence of Frobenius norm regularized logistic loss functions as Villani functions, proving convergence and exponential rate.
result SGD converges globally to the global minima of appropriately regularized logistic empirical risk of depth 2 nets.
Gradient flows of neural networks converge to optimal values or diverge, with thresholds and asymptotic behaviors.
problem Understanding the convergence and divergence of gradient flows in neural networks.
method Analysis of gradient flows on loss landscapes of neural networks using o-minimal structures.
result Gradient flows either converge to optimal values or diverge to infinity, with thresholds and asymptotic behaviors.
We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and epistemic uncertainty in a coherent manner. The intractable posterior probability dis…
Neural networks can approximate any L^p functions on R^n.
problem Approximating functions on unbounded domains with neural networks.
method Monotone sigmoid, ReLU, ELU, Softplus, LeakyReLU activation functions.
result Shallow neural networks can arbitrarily well approximate L^p functions on R^n.
Global convergence of SGD proven for two-layer neural nets with regularization.
problem Proving global convergence of SGD for two-layer neural nets.
method Regularized empirical risk, SGD iterates, Villani functions.
result Global convergence of SGD for a special class of initializations.
Improved variational inference for logistic regression and classification.
problem Intractability of Evidence Lower Bound in variational logistic regression.
method Introducing a new bound for the expectation of softplus function, applied to variational logistic regression and Gaussian process classification.
result The new bound results in a tighter posterior and faster computation compared to Monte-Carlo methods.
Deep networks can approximate various activation functions with modest adjustments.
problem Expressive power of deep neural networks with diverse activation functions.
method Approximation of any activation function in set A by ReLU networks with specific scaling factors.
result Approximation of any activation function in a specific subset of A by ReLU networks with (1,1) scaling factors.
This work introduces an efficient method to sample high-quality images from conditional GANs.
problem Efficient subsampling of images from conditional GANs (cGANs) is challenging.
method Developed a novel conditional density ratio estimation method (cDRE-F-cSP) and rejection sampling scheme (cDR-RS).
result cDR-RS outperforms state-of-the-art methods in both effectiveness and efficiency.
New algorithm reduces sample complexity for learning CNNs.
problem Learning one-hidden-layer CNNs with various activation functions.
method Approximate gradient descent algorithm for training CNNs.
result Sample complexity matches information-theoretic lower bound for linear activation functions.
A neural network derived from first principles using MaxEnt.
problem Developing a neural network from first principles.
method Derived a neural network using the principle of Maximum Entropy, with linear dimension-reducing transformations and conditional mean estimators.
result Unified theoretical justification for activation functions like sigmoid, softplus, and relu.
AGGLIO optimizes non-convex functions with local convexity guarantees.
problem Optimizing non-convex functions with local convexity.
method Stage-wise, graduated optimization technique for locally convex functions.
result Global convergence to the global optimum for non-convex and locally convex objectives.
Using back-propagation and its variants to train deep networks is often problematic for new users. Issues such as exploding gradients, vanishing gradients, and high sensitivity to weight initialization strategies often make networks difficult to train, especially when users are experimenting with new architectures. Her…
We propose Mish, a novel self-regularized non-monotonic activation function which can be mathematically defined as: f(x)=xtanh(softplus(x)). As activation functions play a crucial role in the performance and training dynamics in neural networks, we validated experimentally on several well-known benchmarks…
Adaptive gradient methods (AGMs) have become popular in optimizing the nonconvex problems in deep learning area. We revisit AGMs and identify that the adaptive learning rate (A-LR) used by AGMs varies significantly across the dimensions of the problem over epochs (i.e., anisotropic scale), which may lead to issues in c…
This research improves neural network performance with adaptive activation functions in sparse data settings.
problem Limited data availability in scientific and engineering problems.
method Investigation of two types of adaptive activation functions with individual trainable parameters.
result Adaptive activation functions, especially with individual trainable parameters, enhance prediction accuracy and confidence in sparse data settings.
Lower bound proves ridgeless regression performs poorly near interpolation threshold.
problem Proving performance of ridgeless regression near interpolation threshold.
method Distribution-independent lower bound for mean squared error in noisy ridgeless linear regression.
result Lower bound implies ridgeless regression performs poorly near interpolation threshold.
Quantized neural networks can represent all fixed-point functions under certain conditions.
problem Expressive power of quantized neural networks under fixed-point arithmetic.
method Analyzing necessary and sufficient conditions for quantized networks to represent all fixed-point functions.
result Various popular activation functions satisfy the sufficient condition for representing all fixed-point functions.
Minimum width for ReLU networks on compact domain is exactly max{d_x, d_y, 2}
problem Characterizing the minimum width for ReLU networks to approximate functions on compact domains
method Analyzing the minimum width for Lp approximation of Lp functions from [0,1]d to Rdy using ReLU-like activation functions result The minimum width for Lp approximation on a compact domain is exactly max{d_x, d_y, 2} for ReLU-like activation functions IGNIS uses neural networks to estimate copula parameters robustly.
problem Pathological properties of Archimedean copulas make traditional estimators brittle.
method Unified neural estimation framework with multi-input architecture and softplus output layer.
result Accurate and stable estimates for real-world datasets.
Imitation learning is a control design paradigm that seeks to learn a control policy reproducing demonstrations from expert agents. By substituting expert demonstrations for optimal behaviours, the same paradigm leads to the design of control policies closely approximating the optimal state-feedback. This approach requ…
We develop embeddings for nonlinear subspaces preserving vector norms.
problem Preserving vector norms in nonlinear subspaces.
method Low-distortion embeddings for subspaces under nonlinear transformations.
result First low-distortion embeddings for a wide class of nonlinear functions.
This paper proposes a continuous timing strategy for growth vs. defensive style allocation.
problem Dynamic allocation of growth and defensive ETF baskets using macro-market timing signals.
method Continuous smooth score combining multiple factors, mapped to G/D weights, smoothed with EWMA.
result Continuous style timing strategy outperforms static benchmarks in risk-adjusted returns.
Introduces Fitzpatrick losses, tighter than Fenchel-Young losses.
problem Improving loss functions for machine learning.
method Introduces Fitzpatrick losses based on the Fitzpatrick function.
result Fitzpatrick losses are tighter than Fenchel-Young losses.
We study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function. We characterise when margin losses can be proper composite losses, explicitly show how to determ…
We present the Tamed Cross Entropy (TCE) loss function, a robust derivative of the standard Cross Entropy (CE) loss used in deep learning for classification tasks. However, unlike other robust losses, the TCE loss is designed to exhibit the same training properties than the CE loss in noiseless scenarios. Therefore, th…
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.
This paper introduces new loss functions for balanced multi-class classification.
problem Balancing class imbalance in multi-class classification.
method Introduces two new surrogate loss families: GLA and GCA.
result GCA losses offer stronger theoretical guarantees in imbalanced settings.
We present α-loss, α∈[1,∞], a tunable loss function for binary classification that bridges log-loss (α=1) and 0-1 loss (α=∞). We prove that α-loss has an equivalent margin-based form and is classification-calibrated, two desirable properties for a good surrogate loss function for the ideal y…
This work broadens calibeating to various proper losses using Bregman divergence.
problem Calibration for a wide range of proper losses.
method Regret minimization and Bregman divergence approach.
result U-calibration results for a family of Tsallis losses with logarithmic regret and dimension independence.
This work generalizes calibeating for a broader range of proper losses using Bregman divergence.
problem Calibration for a wide range of proper losses beyond Brier and log loss.
method Regret minimization based on Bregman divergence for a family of proper losses.
result U-calibration results for a family of Tsallis losses with logarithmic regret and dimension independence.
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.
New loss function calibrates WW-hinge loss for multiclass SVM.
problem WW-hinge loss not calibrated with 0-1 loss.
method Introduced ordered partition loss and proved WW-hinge loss is calibrated.
result WW-hinge loss is calibrated with ordered partition loss.
The study analyzes a model for aggregate losses with dependent and overdispersed inter-losses times.
problem Analyzing aggregate loss models with dependent and overdispersed inter-losses times.
method The study uses a two-state Markovian arrival process (MAP2) and a Markov renewal process to model the inter-losses times. Severities are modeled using a heavy-tailed, double-Pareto Lognormal distribution. The model is estimated via direct maximization of the likelihood function.
result The model with dependence and overdispersion in inter-losses times leads to higher capital charges compared to a Poisson process.
Symmetric losses improve classifier robustness from corrupted labels.
problem Improving classifier performance from corrupted labels.
method Symmetric losses that satisfy a certain condition.
result Symmetric losses enhance robust classification from corrupted labels.
Two new algorithms improve performance in adversarial bandits with unbounded losses.
problem Adversarial Multi-Armed Bandits with unbounded losses.
method Developed UMAB-NN and UMAB-G for non-negative and general unbounded losses respectively.
result UMAB-NN achieves the first adaptive and scale-free regret bound for non-negative unbounded losses.
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.
Paper introduces a new topological loss for better convergence.
problem Optimizing topological losses for model's desired topological behavior.
method Introduces a new regularized topology-aware loss function.
result Guarantees efficient optimization of the new loss function.
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.
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. This paper improves operational risk modeling by selecting better loss severity distributions.
problem Inconsistent regulatory capital calculations due to changing loss severity distribution families.
method Presented truncation probability estimates and a consistent quantile scoring function for selection criteria. Also, recommended collecting loss frequencies below the minimum reporting threshold.
result More stable regulatory capital calculations through better selection of loss severity distributions.
This paper improves loss functions for deep learning with noisy labels.
problem Training deep neural networks with noisy labels.
method The paper introduces a normalization technique to make any loss function robust to noisy labels and proposes a framework called Active Passive Loss (APL) to combine robust loss functions.
result The proposed APL framework consistently outperforms state-of-the-art methods, especially under high noise rates.
Classification is the most important process in data analysis. However, due to the inherent non-convex and non-smooth structure of the zero-one loss function of the classification model, various convex surrogate loss functions such as hinge loss, squared hinge loss, logistic loss, and exponential loss are introduced. T…
We study cross-country GDP losses due to financial crises in terms of frequency (number of loss events per period) and severity (loss per occurrence). We perform the Loss Distribution Approach (LDA) to estimate a multi-country aggregate GDP loss probability density function and the percentiles associated to extreme eve…
The paper proves deep learning can be robust with certain loss functions.
problem The robustness of deep learning models under flawed data.
method Empirical-risk minimization with unbounded, Lipschitz-continuous loss functions.
result These loss functions provide efficient prediction under minimal data assumptions.