Survey of spectral, probabilistic, and deep metric learning methods.
problem Developing effective distance metrics for various machine learning tasks.
method Divided into spectral, probabilistic, and deep approaches, covering various techniques and their applications.
result Comprehensive overview of metric learning methods, including new developments and applications.
Research connects probabilistic and variational approaches to Kahler-Einstein metrics.
problem Constructing Kahler-Einstein metrics on complex projective varieties.
method Combines probabilistic construction and variational methods.
result Non-Archimedean geometry of X emerges from probabilistic framework.
New scoring rules compare probabilistic top lists in classification.
problem Evaluation of probabilistic top lists in classification.
method Elicitability through symmetric proper scoring rules.
result Brier score provides a well-suited metric for comparison.
New metrics improve probabilistic forecasting, especially for rare events.
problem Current evaluation frameworks for probabilistic forecasting assume independence and lack sensitivity to tail events.
method Proposed signature kernel-based metrics: Sig-MMD and CSig-MMD.
result These metrics capture complex dependencies and prioritize tail event prediction.
Small neural networks embed arbitrary metric spaces into Gaussian mixtures.
problem Embedding arbitrary metric spaces into a fixed space with low distortion.
method Probabilistic transformers of small depth and width.
result Embeddings with low metric distortion for various metric spaces.
A new probabilistic approach improves deep metric learning by considering image uncertainties and class-specific variances.
problem Proxy-based deep metric learning struggles with image uncertainties and class-specific structures.
method Introduces non-isotropic probabilistic proxy-based deep metric learning using directional von Mises-Fisher distributions.
result Improves generalization performance and competitive on standard benchmarks.
This paper improves probabilistic latent models on hyperbolic spaces.
problem Uncertainty in predictions due to geodesics crossing low-data regions.
method Augmenting hyperbolic manifold with a pullback metric for probabilistic pullback metrics.
result Geodesics on pullback metric respect both geometry and data distribution, reducing uncertainty.
New probabilistic constructions for Kähler-Einstein metrics.
problem Finding Kähler-Einstein metrics on complex algebraic varieties.
method Microcanonical measures and maximum entropy principles.
result Novel characterizations and evolution equations.
New probabilistic method constructs Kähler-Einstein metrics and suggests zero-free properties of zeta functions.
problem Existence and explicit formulas for Kähler-Einstein metrics on Fano varieties.
method Probabilistic construction involving canonical random point processes.
result Zero-free properties of Archimedean zeta functions and their relation to Langlands program.
This paper improves QoS metric prediction in DTNs using diffusion models.
problem Improving QoS metric prediction in Delay-Tolerant Networks (DTNs) to enhance network performance.
method Formulates QoS metric prediction as a probabilistic forecasting problem on multivariate time series, incorporating latent temporal dynamics.
result The proposed approach outperforms traditional methods in QoS metric prediction for DTNs.
A novel GPUM constructs Gaussian Processes for unknown manifolds with probabilistic metrics.
problem High-dimensional data on unknown manifolds with non-Euclidean geometry.
method Bayesian Gaussian Processes latent variable models (BGPLVM), Riemannian geometry, probabilistic metric tensor, Brownian Motion.
result GPUM provides more accurate predictions on unknown manifolds compared to traditional methods.
New k-means method handles random data better than traditional techniques.
problem Limitations of traditional clustering methods in random data.
method Probabilistic metric space with random normed k-means (RNKM).
result RNKM outperforms traditional methods in complex clustering scenarios.
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where the distribution over…
Invites probabilistic approach to Kähler-Einstein metrics via random point processes.
problem Constructing Kähler-Einstein metrics on complex projective algebraic manifolds.
method Large N-limit from random point processes defined by algebro-geometric data; variational approach for positive Ricci curvature.
result Convergence of metrics to Kähler-Einstein metrics under specific conditions.
Probabilistic fair clustering tackles uncertain group membership.
problem Fair clustering with imperfect group membership.
method Probabilistic algorithms for metric graphs and metric membership.
result Approximation ratio guarantees for fair clustering.
New bound on partition function proves Kähler-Einstein stability.
problem Proving Kähler-Einstein metrics on complex manifolds.
method Quantitative bound on partition function, connecting probabilistic and quantization approaches.
result Direct analytic proof of Kähler-Einstein stability for uniformly Gibbs stable manifolds.
We prove that the Euler form of a metric connection on real oriented vector bundle E over a compact oriented manifold M can be identified, as a current, with the expectation of the random current defined by the zero-locus of a certain random section of the bundle. We also explain how to reconstruct probabilisticall…
New method classifies manifold-valued data using Riemannian geometry.
problem Classifying data on curved Riemannian manifolds.
method Probabilistic Learning Vector Quantization on Symmetric Positive Definite Matrices.
result The method outperforms traditional Euclidean methods on manifold-valued data.
Kernel quadrature improves CRPS estimation for probabilistic time-series forecasting.
problem Intractable integrations in CRPS evaluation metrics lead to improper rankings of forecasting models.
method Introduced kernel quadrature approach for unbiased CRPS estimation and scalable computation.
result Our approach consistently outperforms existing CRPS estimators.
Proposes CCE to assess point-wise reliability of neural network predictions.
problem Overconfidence and misaligned predictive distributions in neural networks.
method Introduces Conditional Congruence (CCE) metric using conditional kernel mean embeddings.
result CCE exhibits correctness, monotonicity, reliability, and robustness in high-dimensional regression tasks.
State-space systems generate probabilistic dependencies between inputs and outputs.
problem Understanding probabilistic dependencies in state-space systems.
method Introducing a probabilistic framework and proving sufficient conditions for output existence and uniqueness.
result State-space systems can generate probabilistic dependencies, even without functional relations.
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal quantization, and learning theory, we derive new probabilistic bounds for the per…
Proposes a new metric learning method for image recognition.
problem Improving image recognition performance using learned distance representations.
method Introduces a Generalized Hybrid Metric Loss (GHM-Loss) to learn hybrid proximity features combining geometric and probabilistic spaces.
result Demonstrates superior performance compared to existing methods on public datasets.
Proposes deep mixture models for probabilistic price movement forecasting in high-frequency trading.
problem Probabilistic forecasting of price movements in high-frequency trading.
method Deep recurrent neural networks with probabilistic mixture models.
result Outperforms benchmark models in both metric-based and simulated trading scenarios.
Paper presents a new video generation model using diffusion probabilistic methods.
problem Generating high-quality video sequences.
method Denoising diffusion probabilistic models, autoregressive, end-to-end optimization.
result Significant improvements in perceptual quality and probabilistic frame forecasting.
ProBoost boosts probabilistic classifiers by focusing on uncertain samples.
problem Improving probabilistic classifiers through targeted learning.
method ProBoost uses epistemic uncertainty to select challenging samples, increasing their weight for subsequent learners.
result ProBoost significantly improves classifier performance, especially with few weak learners.
Introduces Rashomon Capacity to measure predictive multiplicity in probabilistic classifiers.
problem Predictive multiplicity in classification models leading to unjustified decisions.
method Introduces Rashomon Capacity, a metric for probabilistic classifiers, and provides a rigorous derivation.
result Rashomon Capacity captures nuanced score variations and provides strategies for disclosing conflicting models.
This research focuses on invariant probabilistic predictions, showing they are not robust under distribution shifts.
problem The challenge of creating robust probabilistic predictions that remain consistent under distribution shifts.
method A causality-inspired framework to investigate invariance and robustness of probabilistic predictions with respect to proper scoring rules.
result Arbitrary distribution shifts do not admit invariant and robust probabilistic predictions, unlike point predictions.
Study optimizes tree-based models for better alignment of predicted scores and actual probabilities.
problem Traditional calibration metrics fail to align predicted scores with actual probabilities when score distributions deviate from the underlying data.
method Optimizes tree-based models (Random Forest, XGBoost) using Kullback-Leibler (KL) divergence to minimize the difference between predicted and true probability distributions.
result Optimized tree-based models yield superior alignment between predicted scores and actual probabilities without significant performance loss.
SAMBA improves safe reinforcement learning with active exploration metrics.
problem Safe reinforcement learning in dynamic systems.
method Combines probabilistic modelling, information theory, and statistics. Uses novel metrics for out-of-sample Gaussian process evaluation.
result Orders of magnitude reduction in samples and violations compared to state-of-the-art methods.
Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller manifold. Additionally, in these applications the Euclidean geometry might induc…
Rigorous uncertainty quantification of probabilistic AI weather forecasts with conformal prediction
problem Calibrated uncertainty quantification in probabilistic weather forecasts
method Conformal prediction
result Calibrated uncertainty at no expense to other probabilistic metrics
Probabilistic Autoencoder learns latent space weights' distribution.
problem Nonlinear model reconstruction error and sample quality.
method Normalizing flow for latent space weights' probability distribution.
result PAE achieves small reconstruction errors, high sample quality, and good performance.
We show that Bonnesen's isoperimetic defect has a systolic analog for Loewner's torus inequality. The isosystolic defect is expressed in terms of the probabilistic variance of the conformal factor of the metric g with respect to the flat metric of unit area in the conformal class of g.
It is often observed that the probabilistic predictions given by a machine learning model can disagree with averaged actual outcomes on specific subsets of data, which is also known as the issue of miscalibration. It is responsible for the unreliability of practical machine learning systems. For example, in online adve…
Unified approach for fair classification with overlapping groups.
problem Ensuring fairness across multiple overlapping groups in prediction problems.
method Probabilistic population analysis leading to Bayes-optimal classifier, unifying existing methods.
result Outperforms baselines in fairness-performance tradeoff on real datasets.
Network metrics form a fundamental part of the network analysis toolbox. Used to quantitatively measure different aspects of the network, these metrics can give insights into the underlying network structure and function. In this work, we connect network metrics to modern probabilistic machine learning. We focus on the…
We analyze the probabilistic variance of a solution of Liouville's equation for curvature, given suitable bounds on the Gaussian curvature. The related systolic geometry was recently studied by Horowitz, Katz, and Katz, where we obtained a strengthening of Loewner's torus inequality containing a "defect term", similar …
This paper introduces a new metric for deep learning networks based on their classification performance.
problem The mystery and black-box nature of deep learning networks.
method Proposes a new distance measure based on the probabilistic performance of deep learning networks.
result The proposed metric space is compact and coincides with the quotient topological space.
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this paper, we provide a probabilistic graphical model for reciprocal processes. This le…
This work proposes using Conformal Prediction to improve OOD detection scores and vice versa.
problem Improper evaluation of OOD detection scores due to finite sample size.
method Defining new conformal AUROC and FRP@TPR95 metrics and using OOD scores as non-conformity scores.
result Improved evaluation metrics and better interpretation of OOD scores.
Proposes a deep learning model for probabilistic forecasting that is also interpretable.
problem Inability to explain predictions of neural network-based time series forecasting methods.
method Deep Autoregressive Networks (DANLIP) for locally interpretable probabilistic forecasting.
result DANLIP provides interpretable predictions with comparable performance to state-of-the-art methods.
Paper proposes a method for weather-informed probabilistic forecasting and scenario generation in power systems.
problem Challenges of integrating renewable energy sources into power grids due to their stochasticity and uncertainty.
method Combines probabilistic forecasting and Gaussian copula for day-ahead prediction and scenario generation of load, wind, and solar power.
result Demonstrates superior performance of the proposed weather-informed Temporal Fusion Transformer (WI-TFT) model.
Develops methods to measure and reduce fairness in datasets with limited protected attribute labels.
problem Measuring and reducing fairness in datasets with limited protected attribute labels.
method Proposes methods to estimate fairness metrics and train models to limit fairness violations using probabilistic protected attribute labels.
result Our methods provide tighter bounds on true disparity and effectively reduce fairness violations with lesser fairness-accuracy trade-offs.
A framework assesses the trustworthiness of probabilistic classifiers using local calibration error.
problem Assessing the trustworthiness of probabilistic classifiers beyond traditional metrics.
method I-trustworthy framework linking local calibration to trustworthiness; Kernel Local Calibration Error (KLCE) method for hypothesis testing.
result The effectiveness of the proposed test statistic demonstrated through simulated and real-world datasets.
Adaptive volatility method improves probabilistic financial forecasting.
problem Probabilistic forecasting in financial markets.
method Adapts classical time-varying volatility models with online stochastic optimization.
result Ranked 5th in M6 financial forecasting competition.
Paper presents a probabilistic diagnostic model for identifying and treating supervised learning degradation issues.
problem Degradation problems in supervised learning, including class imbalance, overlapping, small-disjuncts, noisy labels, and sparseness.
method Develops a novel probabilistic diagnostic model to identify and treat degradation issues in supervised learning.
result Early and correct diagnosis of degradation issues allows for selecting appropriate remediation treatments and unbiased performance metrics.
This review explores probabilistic forecasting methods in evolving energy markets.
problem Volatility and uncertainty in renewable energy markets require probabilistic forecasting for risk assessment.
method Traces evolution from Bayesian and distribution-based approaches to conformal prediction.
result Probabilistic forecasting offers a more comprehensive approach to risk assessment and market participation.