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.
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.
Sharp asymptotics derived for phase retrieval and compressed sensing with random generative priors.
problem Phase retrieval and compressed sensing with random measurement matrices.
method Sharp asymptotics derived for optimal performance and polynomial algorithm for random generative priors.
result Compressed phase retrieval becomes tractable with random generative priors, unlike sparse priors.
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…
New estimator accurately estimates mean of real-valued distributions without variance knowledge.
problem Estimating the mean of real-valued distributions without prior variance knowledge.
method Introduces a novel estimator that converges sub-Gaussian and works across distributions with bounded variance.
result The estimator achieves accuracy of σ·(1+o(1))√(2log(1/δ)/n) with parameters n, δ, and σ².
Hierarchical beta process has found interesting applications in recent years. In this paper we present a modified hierarchical beta process prior with applications to hierarchical modeling of multiple data sources. The novel use of the prior over a hierarchical factor model allows factors to be shared across different …
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.
GPLVMF improves CARS performance by addressing overfitting and context importance.
problem Overfitting and lack of automatic context importance determination in GP-based CARS.
method GPLVMF applies a non-zero mean function and real-valued latent space to improve GP model performance.
result Significant improvement in performance on real datasets and automatic context importance determination.
Extends GP regression to complex Helmholtz problems, improving wavefield inference in brain elastography.
problem Infer complex Helmholtz wavefields from sparse, noisy data.
method Operator-informed Gaussian processes, realifying complex operator into real blocks, using PDE residuals and boundary traces.
result Competitive with finite-difference and neural-network methods, reconstructs brain shear curl field with high correlation.
New Gaussian priors for neural networks improve scalability and Bayesian inference stability.
problem Scalability and stability issues in Bayesian neural network inference.
method Introduces a new Gaussian neural network prior with decreasing variance in network width, enabling stable MCMC sampling.
result The new prior enables stable MCMC sampling for Bayesian neural network inference, improving scalability and stability.
This study examines how discretization improves neural forecasting models.
problem Improving predictive performance of neural forecasting models.
method Empirical investigation of data binning techniques on various neural forecasting architectures.
result Data binning almost always improves forecasting accuracy, but the type of binning is less important.
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.
Paper tackles image recovery from blurry measurements using deep generative priors.
problem Jointly recovering two real-valued signals from phaseless circular convolutions.
method Alternating gradient descent algorithm with deep generative priors.
result Reconstructs quality images from blurry measurements.
A dimension allowing in particular to state necessary and sufficient conditions of the Morse-Sard Theorem for real valued functions is introduced.
Study improves fractional posterior for 1-bit matrix completion.
problem Estimating a binary matrix from observed entries.
method Fractional posterior approach with low-rank factorization and spectral scaled Student priors.
result Concentration results for fractional posterior, demonstrating effectiveness in matrix recovery.
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.
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.
Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained from a fine grid sampling of functional data, all methods benefit from a prior simp…
Optimizing noise variance in VAEs balances reconstruction quality and prior regularisation.
problem Balancing reconstruction quality and prior regularisation in VAEs.
method Learning the noise variance in the Gaussian likelihood to balance the ELBO loss.
result Optimizing noise variance improves VAE-generated sample quality and uncertainty.
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.
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.
New probabilistic model for semi-nonnegative matrix factorization using Skellam distribution.
problem Automatic clustering of semi-nonnegative data.
method Skellam-SNMF model with EM and VBEM algorithms.
result New divergence D and algorithms outperform classic SNMF. 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 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.
New algorithm reduces sample complexity for online reinforcement learning.
problem Reducing sample complexity for online reinforcement learning in nonlinear systems.
method Generalized algorithm for various dynamical systems, including neural networks.
result Achieves policy regret of O(Nε^2 + d_u ln(m(ε))/ε^2) in general settings.
Quantum algorithm estimates mean with sub-Gaussian error.
problem Estimating mean of quantum-computed random variables.
method Quantum mean estimation algorithm with sub-Gaussian error rate.
result Achieves nearly-optimal quadratic speedup over classical methods.
Study connects Gaussian processes and regularization for sequence-function mappings.
problem Understanding and interpreting sequence-function maps in biology.
method Relates Gaussian process priors, regularization, and gauge fixing in overparameterized weight space.
result Established the relationship between regularized regression and Gaussian processes in function space.
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.
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.
ERAPS builds prediction sets for time-series data.
problem Uncertainty quantification in complex machine learning methods for time-series data.
method ERAPS is an ensemble-based framework for constructing prediction sets for time-series data, allowing unknown dependencies within features and responses.
result ERAPS demonstrates valid marginal and conditional coverage and yields smaller prediction sets than competing methods.
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 …
Restricted Boltzmann machines (RBMs) are energy-based neural-networks which are commonly used as the building blocks for deep architectures neural architectures. In this work, we derive a deterministic framework for the training, evaluation, and use of RBMs based upon the Thouless-Anderson-Palmer (TAP) mean-field appro…
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.
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper propo…
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 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…
Generative models improve MRI reconstruction by learning image structure.
problem Improving MRI image quality from undersampled data.
method Using variational autoencoders (VAEs) to learn image structure and covariance.
result The proposed method outperforms other regularization techniques on MRI datasets.
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.
New method detects anomalies in time series data, especially useful for monitoring services.
problem Detecting anomalies in time series data, especially for monitoring services and cloud resources.
method Models time series of probability distributions over real values, scales to millions of time series.
result Outperforms state-of-the-art methods in detecting anomalies on various data sets.
Rotation forest is superior to other classifiers for problems with continuous features.
problem Classifying problems with real-valued features.
method Empirical comparison of classifiers from three families: SVM, tree-based ensembles, and neural networks.
result Rotation forest is significantly more accurate than competing techniques on average.