Related papers: The Geometry of Mixability
Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…
Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a…
In this work we define a metric structure to compare functions defined on different merge trees. The metric introduced possesses some stability properties, which we illustrate within a standard topological data analysis (TDA) framework, and…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
Knowledge graph embedding models (KGEMs) are used for various tasks related to knowledge graphs (KGs), including link prediction. They are trained with loss functions that consider batches of true and false triples. However, different kinds…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
Loss function learning is a new meta-learning paradigm that aims to automate the essential task of designing a loss function for a machine learning model. Existing techniques for loss function learning have shown promising results, often…
Multi-task learning (MTL) is a subfield of machine learning with important applications, but the multi-objective nature of optimization in MTL leads to difficulties in balancing training between tasks. The best MTL optimization methods…
We demonstrate equivalence between the reinforcement learning problem and the supervised classification problem. We consequently equate the exploration exploitation trade-off in reinforcement learning to the dataset imbalance problem in…
Model merging offers a promising avenue for knowledge integration and parallel development without retraining. Yet, existing methods either ignore the geometry of the loss landscape or rely on intractable full-space Hessian approximations.…
Representation learning has been widely studied in the context of meta-learning, enabling rapid learning of new tasks through shared representations. Recent works such as MAML have explored using fine-tuning-based metrics, which measure the…
We observe that incorporating a shared layer in a mixture-of-experts can lead to performance degradation. This leads us to hypothesize that learning shared features poses challenges in deep learning, potentially caused by the same feature…
A novel model called error loss network (ELN) is proposed to build an error loss function for supervised learning. The ELN is in structure similar to a radial basis function (RBF) neural network, but its input is an error sample and output…
Link Prediction (LP) is a critical task in graph machine learning. While Graph Neural Networks (GNNs) have significantly advanced LP performance recently, existing methods face key challenges including limited supervision from sparse…
We revisit the classical problem of deriving convergence rates for the maximum likelihood estimator (MLE) in finite mixture models. The Wasserstein distance has become a standard loss function for the analysis of parameter estimation in…
Many evaluation metrics can be used to assess the performance of models in binary classification tasks. However, most of them are derived from a confusion matrix in a non-differentiable form, making it very difficult to generate a…
This paper presents a comprehensive review of loss functions and performance metrics in deep learning, highlighting key developments and practical insights across diverse application areas. We begin by outlining fundamental considerations…
We propose a general approach for supervised learning with structured output spaces, such as combinatorial and polyhedral sets, that is based on minimizing estimated conditional risk functions. Given a loss function defined over pairs of…
Glass-like objects can be seen everywhere in our daily life which are very hard for existing methods to segment them. The properties of transparencies pose great challenges of detecting them from the chaotic background and the vague…
The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting…