The study examines non-continuous Riemannian metrics on manifolds and their infinitesimal properties.
problem Investigating non-continuous Riemannian metrics and their infinitesimal structure.
method Constructing examples of metric measure spaces with discontinuous metrics.
result Examples show failure of infinitesimal Hilbertian or quasi-Riemannian properties.
A new clustering model for mixed datasets combines continuous and non-continuous data.
problem Challenges in clustering mixed data due to heterogeneous variables.
method Mixed Deep Gaussian Mixture Model (MDGMM) with multilayer architecture.
result Automatic selection of model specifications and optimal number of clusters.
We propose a robust adversarial prediction framework for general multiclass classification. Our method seeks predictive distributions that robustly optimize non-convex and non-continuous multiclass loss metrics against the worst-case conditional label distributions (the adversarial distributions) that (approximately) m…
We study the problem of attacking a machine learning model in the hard-label black-box setting, where no model information is revealed except that the attacker can make queries to probe the corresponding hard-label decisions. This is a very challenging problem since the direct extension of state-of-the-art white-box at…
Geometrically, twist numbers on punctured tori are dense and non-continuous.
problem Understanding twist numbers on hyperbolic punctured tori.
method Hyperbolic geometry and Farey graph analysis.
result The graph of twist numbers is dense in [0,1]x[0,1].
Recent advances in derivative-free optimization allow efficient approximation of the global-optimal solutions of sophisticated functions, such as functions with many local optima, non-differentiable and non-continuous functions. This article describes the ZOOpt (Zeroth Order Optimization) toolbox that provides efficien…
Deep learning models have been successfully used in computer vision and many other fields. We propose an unorthodox algorithm for performing quantization of the model parameters. In contrast with popular quantization schemes based on thresholds, we use a novel technique based on periodic functions, such as continuous t…
We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the portfolio on the date of maturity of the call option we find a fraction of the ass…
A new copula, the checkerboard copula, maximizes entropy and preserves dependence.
problem Choosing copula for non-continuous marginal distributions.
method Introducing the checkerboard copula, maximizing Shannon entropy.
result Checkerboard copula maximizes entropy and preserves dependence.
The paper explores fair treatment in financial exchanges, finding unbounded fairness unrealistic and proposing ε-fairness as a solution.
problem Ensuring fair treatment of all competing participants in financial exchanges.
method Investigation of unbounded temporal fairness, analysis of real-world incidents, introduction of ε-fairness.
result Unbounded temporal fairness is unrealistic in FIFO markets, and ε-fairness provides a viable alternative.
Researchers created a continuous Markov martingale that mimics Brownian motion but lacks the strong Markov property.
problem Constructing a continuous Markov martingale with Brownian marginals that misses the strong Markov property.
method Developed a new approach to create a continuous Markov martingale that differs from Brownian motion in terms of the strong Markov property.
result A continuous Markov martingale with Brownian marginals that lacks the strong Markov property was successfully constructed.
Survey of Fermat principle in general relativity and beyond.
problem Mathematical challenges in variational formulation of Fermat principle in Lorentzian geometry.
method Proof in smooth lightlike curves, analysis of null condition, alternative frameworks, multiplicity results.
result Space of lightlike curves does not admit a smooth manifold structure due to cone nature of null condition.
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape, researchers in practice areas such as marketing and social sciences also frequen…
MMM model clusters mixed-type longitudinal data efficiently.
problem Challenges in clustering multivariate longitudinal mixed-type data.
method MMM model reorganizes data into a three-way structure, using a mixture of matrix-variate normal distributions.
result MMM model handles various data types (continuous, ordinal, binary, nominal, count) and temporal dependence.
Optimal transport kernels improve neural architecture search efficiency.
problem Comparing complex neural architectures similarity using Euclidean metric fails.
method Developed a novel discrepancy using tree-Wasserstein (TW) for neural architectures.
result TW-based approaches outperform other methods in sequential and parallel NAS.
Generative models enhance BO for large batch optimization.
problem Efficiently sampling solutions in high-dimensional, combinatorial design spaces.
method Train generative models to sample solutions proportional to expected utility.
result Generative models can approximate optimal target distributions under certain conditions.
Variational autoencoder (VAE) is a deep generative model for unsupervised learning, allowing to encode observations into the meaningful latent space. VAE is prone to catastrophic forgetting when tasks arrive sequentially, and only the data for the current one is available. We address this problem of continual learning …
Modern machine learning uses more and more advanced optimization techniques to find optimal hyper parameters. Whenever the objective function is non-convex, non continuous and with potentially multiple local minima, standard gradient descent optimization methods fail. A last resource and very different method is to ass…
Study the hedging of cryptocurrency options in a volatile market.
problem Hedging options in a volatile, non-stationary cryptocurrency market.
method Calibrated to SVI-implied volatility surfaces, Monte Carlo price paths generated using SVCJ, GARCH, and historical data. Delta, Delta-Gamma, Delta-Vega, and Minimum Variance strategies applied. Wide range of market models tested.
result Calibration results indicate stochastic volatility, low jump frequency, and infinite activity. Short-dated options less sensitive to volatility or Gamma hedges; longer-dated options benefit from multiple-instrument hedges.
TRESNET estimates exposure shifts with neural networks, improving causal inference.
problem Estimating the effect of distribution shift in treatment variables.
method Targeted Regularization for Exposure Shifts with Neural Networks (TRESNET).
result TRESNET provides robustness and efficiency guarantees for SRF estimation.
LSGM trains SGMs in latent space for faster sampling.
problem Efficiently generating high-quality samples from complex distributions.
method LSGM trains SGMs in latent space using a variational autoencoder framework, introducing new score-matching objectives and parameterizations.
result LSGM achieves state-of-the-art FID score of 2.10 on CIFAR-10 and outperforms previous SGMs in sampling time.
This paper tackles overfitting in CTR models by introducing Multi-Epoch learning with Data Augmentation.
problem Overfitting of the embedding layer in CTR models during multi-epoch training.
method Introduces Multi-Epoch learning with Data Augmentation (MEDA) framework to reduce overfitting and enhance performance.
result MEDA minimizes overfitting and achieves data augmentation through varied embedding spaces, improving performance without overfitting.
The paper explores transferability of adversarial examples between convex and 01 loss models, finding non-transferability due to different decision boundaries caused by outliers.
problem Transferability of adversarial examples between convex and 01 loss models.
method Empirical study of transferability between linear 01 loss and convex (hinge) loss models, and between neural networks with different activation functions.
result Adversarial examples are non-transferable between convex and 01 loss models due to different decision boundaries caused by outliers.