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 dirichlet distribution




Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness

Neural Information Processing Systems

Ensemble approaches for uncertainty estimation have recently been applied to the tasks of misclassification detection, out-of-distribution input detection and adversarial attack detection. Prior Networks have been proposed as an approach to efficiently emulate an ensemble of models for classification by parameteris-ing a Dirichlet prior distribution over output distributions.




Evidential Deep Learning to Quantify Classification Uncertainty

Neural Information Processing Systems

Deterministic neural nets have been shown to learn effective predictors on a wide range of machine learning problems. However, as the standard approach is to train the network to minimize a prediction loss, the resultant model remains ignorant to its prediction confidence. Orthogonally to Bayesian neural nets that indirectly infer prediction uncertainty through weight uncertainties, we propose explicit modeling of the same using the theory of subjective logic. By placing a Dirichlet distribution on the class probabilities, we treat predictions of a neural net as subjective opinions and learn the function that collects the evidence leading to these opinions by a deterministic neural net from data. The resultant predictor for a multi-class classification problem is another Dirichlet distribution whose parameters are set by the continuous output of a neural net. We provide a preliminary analysis on how the peculiarities of our new loss function drive improved uncertainty estimation. We observe that our method achieves unprecedented success on detection of out-of-distribution queries and endurance against adversarial perturbations.


Identifying counterfactual probabilities using bivariate distributions and uplift modeling

Verhelst, Théo, Bontempi, Gianluca

arXiv.org Artificial Intelligence

Uplift modeling estimates the causal effect of an intervention as the difference between potential outcomes under treatment and control, whereas counterfactual identification aims to recover the joint distribution of these potential outcomes (e.g., "Would this customer still have churned had we given them a marketing offer?"). This joint counterfactual distribution provides richer information than the uplift but is harder to estimate. However, the two approaches are synergistic: uplift models can be leveraged for counterfactual estimation. We propose a counterfactual estimator that fits a bivariate beta distribution to predicted uplift scores, yielding posterior distributions over counterfactual outcomes. Our approach requires no causal assumptions beyond those of uplift modeling. Simulations show the efficacy of the approach, which can be applied, for example, to the problem of customer churn in telecom, where it reveals insights unavailable to standard ML or uplift models alone.


Mind the Gap: Bridging Prior Shift in Realistic Few-Shot Crop-Type Classification

Reuss, Joana, Gikalo, Ekaterina, Körner, Marco

arXiv.org Artificial Intelligence

Real-world agricultural distributions often suffer from severe class imbalance, typically following a long-tailed distribution. Labeled datasets for crop-type classification are inherently scarce and remain costly to obtain. When working with such limited data, training sets are frequently constructed to be artificially balanced -- in particular in the case of few-shot learning -- failing to reflect real-world conditions. This mismatch induces a shift between training and test label distributions, degrading real-world generalization. To address this, we propose Dirichlet Prior Augmentation (DirPA), a novel method that simulates an unknown label distribution skew of the target domain proactively during model training. Specifically, we model the real-world distribution as Dirichlet-distributed random variables, effectively performing a prior augmentation during few-shot learning. Our experiments show that DirPA successfully shifts the decision boundary and stabilizes the training process by acting as a dynamic feature regularizer.


Evidential Deep Learning to Quantify Classification Uncertainty

Neural Information Processing Systems

Deterministic neural nets have been shown to learn effective predictors on a wide range of machine learning problems. However, as the standard approach is to train the network to minimize a prediction loss, the resultant model remains ignorant to its prediction confidence. Orthogonally to Bayesian neural nets that indirectly infer prediction uncertainty through weight uncertainties, we propose explicit modeling of the same using the theory of subjective logic. By placing a Dirichlet distribution on the class probabilities, we treat predictions of a neural net as subjective opinions and learn the function that collects the evidence leading to these opinions by a deterministic neural net from data. The resultant predictor for a multi-class classification problem is another Dirichlet distribution whose parameters are set by the continuous output of a neural net. We provide a preliminary analysis on how the peculiarities of our new loss function drive improved uncertainty estimation. We observe that our method achieves unprecedented success on detection of out-of-distribution queries and endurance against adversarial perturbations.