The paper tackles continuous ranking problems with real-valued labels.
problem Continuous ranking with real-valued labels.
method Formulated as optimization of IROC curve or maximization of Kendall τ.
result Proposed a recursive statistical learning algorithm for empirical IROC curve optimization.
Efficient algorithms learn from coarse labels instead of fine grained ones.
problem Learning from coarse labels when fine labels are unavailable.
method Formalized coarse label settings, used a reduction for SQs, and provided efficient algorithms.
result Any problem learnable from fine labels can be learned efficiently from coarse labels.
Paper estimates FPR of Bayes classifier using soft labels.
problem Determining optimal classifier performance.
method Uses soft labels and denoising technique.
result Consistent and unbiased FPR estimator developed.
Algorithm identifies and corrects noisy labels using Gaussian process regression.
problem Detecting and correcting real-valued noisy labels from mixed data.
method Gaussian process regression with heteroscedastic noise model and leave-one-out cross-validation.
result The method can pinpoint corrupted sample points and improve regression models.
Complex-valued neural networks perform similarly to real-valued models for real-valued classification tasks.
problem Comparing real-valued and complex-valued neural networks for real-valued classification tasks.
method Comparison of neural networks with similar capacity sizes, using various activation functions and weight initialisation strategies.
result Complex-valued neural networks perform equal to or slightly worse than real-valued models for real-valued classification tasks.
Study online learning with set-valued feedback, showing differences between deterministic and randomized approaches.
problem Online learning with set-valued feedback, where labels are sets rather than single labels.
method Introduced new combinatorial dimensions (Set Littlestone and Measure Shattering) to characterize learnability.
result Characterized deterministic and randomized online learnability, and established bounds for various learning settings.
Active learning improves soft sensor development by suggesting informative labels.
problem Expensive labeling of process variables in industrial settings.
method Adapted active learning strategies for online data streams and used semi-supervised autoencoders.
result Improved predictive performance of soft sensors using active learning and autoencoders.
Extends Tanimoto kernel to real-valued functions.
problem Measuring similarity between real-valued functions.
method Unified representation of real-valued functions via sets, derived general form of the kernel, explicit feature representation, and smooth approximation.
result General Tanimoto kernel for real-valued functions.
A dimension allowing in particular to state necessary and sufficient conditions of the Morse-Sard Theorem for real valued functions is introduced.
Real valued homomorphisms on the algebra of smooth functions on a differential space are described. The concept of generators of this algebra is emphasized in this description.
Proposes a new method for MIR using kernel mean embeddings.
problem Multiple instance regression (MIR) where bags contain multiple instances with a single label.
method Computes kernel mean embeddings of predicted label distributions and learns a regressor from these embeddings.
result Better results than baseline instance-MIR across all datasets, state-of-the-art on two.
New method attacks black-box models with fewer queries.
problem Attacking machine learning models without model information.
method Formulated as a real-valued optimization problem, solved with zeroth order optimization.
result Demonstrated to outperform random walk approach on various datasets.
Study introduces indecomposability for varifolds, leading to geometric consequences.
problem Understanding the structure of varifolds and their connectedness properties.
method Introducing indecomposability and related concepts for varifolds.
result Substantial geometric consequences derived from the connectedness properties of varifolds.
Generative Adversarial Networks (GANs) have shown remarkable success as a framework for training models to produce realistic-looking data. In this work, we propose a Recurrent GAN (RGAN) and Recurrent Conditional GAN (RCGAN) to produce realistic real-valued multi-dimensional time series, with an emphasis on their appli…
Diffeomorphic Time Warping (DiffTW) is a novel method for time series classification that learns a diffeomorphic mapping between time series.
problem Time series classification
method Diffeomorphic Time Warping (DiffTW)
result Outperforms DTW on 60 out of 86 datasets
We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by the vertices of an undirected graph with the similarity between them captured b…
Learning rule consistency tied to non-existence of real-valued measurable cardinals.
problem Consistency of k-NN learning rule in metric spaces.
method Analyzing separable subspaces and density conditions.
result The k-NN classifier's consistency depends on the absence of real-valued measurable cardinals.
Automates subgroup discovery for real-valued targets using prior knowledge.
problem Finding meaningful patterns in high-dimensional, real-valued data.
method Subjective Interestingness framework FORSIED for efficient subgroup discovery.
result Automatically discovers informative subgroups in data for real-valued targets.
The classical Kaehler potential is a real-valued function (KP) such that one can determine a Kaehler (symplectic) structure by differentiating KP. We define a mirror Kaehler potential on Calabi-Yau 3-folds, a real-valued function (MKP) such that one can determine a complex structure by differentiating MKP.
B-CP reduces knowledge graph model size by replacing real-valued embeddings with binary values.
problem Storage inefficiency in vector embeddings for large knowledge graphs.
method Binarized CANDECOMP/PARAFAC (B-CP) decomposition algorithm.
result B-CP reduces model size by more than an order of magnitude while maintaining task performance.
The paper proposes a tree model for interval-valued regression.
problem Learning a real-valued function from interval-valued data.
method Minimizing a margin-based discriminative objective function using a tree structure and dynamic programming.
result The proposed algorithm achieves state-of-the-art speed and accuracy.
The study analyzes decision trees on real and categorical features, deriving bounds on their VC dimension and proposing improved pruning algorithms.
problem Understanding the generalization properties of decision trees on different types of features.
method Introducing partitioning functions, relating them to growth functions and VC dimension, and deriving bounds for decision stumps and trees of various structures.
result Exact VC dimension of decision stumps and improved pruning algorithms for binary trees.
CVNN outperforms RVNN on non-circular data.
problem Classifying complex-valued data with statistical dependence.
method Comparison of CVNN and RVNN on non-circular data.
result CVNN outperforms RVNN in accuracy and generalization.
Efficient algorithm for converting regression to compressed form.
problem Real-valued regression learning and compression.
method Extension of Moran and Yehudayoff's scheme to real-valued hypotheses.
result First general compressed regression result with uniform approximate reconstruction.
A method for disentangling latent variables using weak supervision based on pairwise similarities.
problem Disentangling latent variables without strong supervision.
method Weak supervision through binary or real-valued similarities, applied within a Variational Autoencoder framework.
result Utilizing weak supervision improves disentanglement performance substantially.
New algorithm speeds up ICWS by 20x for real-valued datasets.
problem Efficiency in real-valued data sketching.
method Simplified approach to ICWS algorithm.
result 20x speedup with same quality results.
Study robust regression learning under adversarial attacks.
problem Understanding which function classes are learnable in the presence of adversarial attacks.
method Introduced a novel agnostic sample compression scheme and used fat-shattering dimension to construct adversarially robust sample compression schemes.
result Finite fat-shattering dimension classes are learnable in both realizable and agnostic settings.
These lecture notes provide a self-contained introduction to the mathematical methods required in a Bachelor degree programme in Business, Economics, or Management. In particular, the topics covered comprise real-valued vector and matrix algebra, systems of linear algebraic equations, Leontief's stationary input-output…
FuBIF enhances AD by using real-valued functions for more flexible anomaly detection.
problem Limitations of the Isolation Forest in adaptability and bias.
method Introduces FuBIF, a generalization of IF using real-valued functions for branching in evaluation trees.
result FuBIF significantly improves flexibility and evaluation tree construction.
A new method for MIR in remote sensing without assuming a prime instance per bag.
problem Multiple Instance Regression in remote sensing with high variability.
method Treats each bag as a set of instances and learns to map each bag to its unique label using all instances.
result Outperforms previous state-of-the-art on three real-world datasets.
Model manipulates facial expressions without affecting other attributes.
problem Manipulating specific visual attributes in real scenes without altering others.
method Trains model on nonphotorealistic 3D renders to manipulate facial expressions, preserving other attributes.
result Model can manipulate facial expressions without affecting other attributes like head orientation.
New algorithm identifies optimal actions in large reward spaces efficiently.
problem Finding the best action from a large set of options with minimal trials.
method GenTS-Explore algorithm for real-valued combinatorial pure exploration.
result Achieves optimal sample complexity for large action sets.
RNNs learn combinatorial graph problems with sample complexity bounds.
problem Learning efficient approximations for real-valued combinatorial graph problems.
method Upper bounds the sample complexity for learning real-valued RNNs.
result Real-valued RNNs can be learned with polynomial number of samples.
Study investigates p-Laplacian regularization in semi-supervised learning.
problem Assigning labels to unlabeled data points using a small training subset.
method Random geometric graphs and p-Laplacian regularization to model the task. result Rigorous analysis of ε(n) scaling for asymptotic consistency in semi-supervised learning. The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image processing, quantum physics or multi-class classificationto name a few. Most works…
In a complete Riemannian manifold (M,g) if the hessian of a real valued function satisfies some suitable conditions then it restricts the geometry of (M,g). In this paper we characterize all compact rank-1 symmetric spaces, as those Riemannian manifolds (M,g) admitting a real valued function u such that the …
We generalize the Omori-Yau almost maximum principle of the Laplace-Beltrami operator on a complete Riemannian manifold M to a second-order linear semi-elliptic operator L with bounded coefficients and no zeroth order term. Using this result, we prove some Liouville-type theorems for a real-valued C2 function …
Paper proposes MS-k-NN for improved convergence rate in k-NN classification.
problem Improving convergence rate of k-NN classification methods.
method Proposes MS-k-NN that extrapolates unweighted k-NN estimators to k=0.
result MS-k-NN achieves improved convergence rate under certain conditions.
We propose a general semi-supervised inference framework focused on the estimation of the population mean. As usual in semi-supervised settings, there exists an unlabeled sample of covariate vectors and a labeled sample consisting of covariate vectors along with real-valued responses ("labels"). Otherwise, the formulat…
Unique solutions found for diffusive martingale problems.
problem Finding unique solutions to Cauchy problems for diffusive real-valued strict local martingales.
method Provided sets of smooth functions under local Hölder and Engelbert-Schmidt conditions for unique classical and weak solutions.
result Unique solutions found for specific martingale models.
New algorithms benchmarked for multivariate time series classification.
problem Comparing algorithms for multivariate time series classification.
method Review and comparison of recent MTSC algorithms using the UEA archive.
result HIVE-COTE ensemble is most accurate for MTSC, but dynamic time warping is competitive.
We introduce RNADE, a new model for joint density estimation of real-valued vectors. Our model calculates the density of a datapoint as the product of one-dimensional conditionals modeled using mixture density networks with shared parameters. RNADE learns a distributed representation of the data, while having a tractab…
In this note we prove the a pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space, analogous to Lindenstrauss' pointwise ergodic theorem for real-valued integrable functions on a probability space subject to a probability-preserving action of an amenable l.c.s.c. group, where in the…
The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued signal into its quadrature component. In this paper, we define a probabilistic gene…
The class of affine LIBOR models is appealing since it satisfies three central requirements of interest rate modeling. It is arbitrage-free, interest rates are nonnegative and caplet and swaption prices can be calculated analytically. In order to guarantee nonnegative interest rates affine LIBOR models are driven by no…
The intrinsic geometric properties of generalized Darboux-Manakov-Zakharov systems of semilinear partial differential equations \label{GDMZabstract} \frac{\partial^2 u}{\partial x_i\partial x_j}=f_{ij}\Big(x_k,u,\frac{\partial u}{\partial x_l}\Big), 1\leq i<j\leq n, k,l\in\{1,...,n\} for a real-valued function $u(x_1,.…
The study examines how prior and likelihood choices affect Bayesian matrix factorisation on small datasets.
problem Improving predictive performance of Bayesian matrix factorisation on small datasets.
method Review and comparison of 16 Bayesian matrix factorisation models across four groups: Gaussian-likelihood with real-valued priors, nonnegative priors, semi-nonnegative models, and Poisson-likelihood approaches.
result Poisson models give poor predictions, and nonnegative models are more constrained than real-valued ones.
The paper uses transfinite induction to prove existence in analysis.
problem Proving existence of extremal objects in analysis.
method Iterative procedure over ordinals to increase function and index steps.
result Existence can be proved using a countable number of steps.