Extends neural network training framework to handle noise and uncertainty.
problem Handling noise and uncertainty in neural network training.
method Integrates non-zero aleatoric noise and derives posterior covariance for epistemic uncertainty.
result Derives an estimator for posterior covariance, providing a handle on epistemic uncertainty.
Paper tackles phase retrieval with robust gradient descent for noisy data.
problem Recover signals from magnitude measurements with noise and corruption.
method Robust gradient descent applied to Wirtinger Flow algorithm.
result Improves algorithm's robustness to heavy-tailed noise and adversarial corruption.
The paper examines conditions for linearity in a conditional mean estimator under vector Poisson noise.
problem Conditions for linearity of the conditional mean estimator in vector Poisson noise.
method Analyzes prior distributions and their impact on the conditional mean estimator's linearity.
result The only prior distribution that induces linearity is a product gamma distribution, and non-zero dark current parameter prevents linearity.
New approach to neural networks by incorporating observation noise and arbitrary prior means.
problem Misspecification on noisy data and limitations of NTK-GP equivalence.
method Introducing a regularizer for observation noise and proposing a shifted network for arbitrary prior means.
result Removes key obstacles to practical Gaussian process modeling in neural networks.
Improved bound for Gaussian mechanism in differential privacy.
problem Finding tighter bounds for Gaussian mechanism in differential privacy.
method Presented a new closed form bound for (ε,δ)-differential privacy using zero mean Gaussian noise. result The new bound is always lower and valid for all ε>0. Regularization helps resolve ambiguity in mean-variance models, improving predictive uncertainty quantification.
problem Signal-to-noise ambiguity in overparameterized mean-variance models.
method Statistical field theory framework to explain phase transition.
result Regularization reduces variability and improves predictive uncertainty quantification.
Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through test-time averaging. In this paper, we introduce variance layers, a different k…
A continuing mystery in understanding the empirical success of deep neural networks is their ability to achieve zero training error and generalize well, even when the training data is noisy and there are more parameters than data points. We investigate this overparameterized regime in linear regression, where all solut…
New mechanisms improve differential privacy for scalar queries.
problem Improving differential privacy for scalar, real-valued query functions.
method Mixing multiple Gaussian distributions to satisfy differential privacy.
result Mechanisms yield lower noise amplitudes and variances compared to the analytic Gaussian mechanism.
M2M tackles zero-shot structured noise suppression in images.
problem Structured noise with strong anisotropic correlations in real-world images.
method M2M introduces a novel sampling strategy that generates pseudo-independent sub-image pairs from a single noisy input, using directional interpolation and generalized median filtering.
result M2M consistently outperforms state-of-the-art zero-shot methods under correlated noise.
The exact meaning of the noise spectrum of eigenvalues of the covariance matrix is discussed. In order to better understand the possible phenomena behind the observed noise, the spectrum of eigenvalues of the covariance matrix is studied under a model where most of the true eigenvalues are zero and the parameters are n…
Paper improves volatility estimation using a Queue-Reactive model.
problem Volatility estimation from high-frequency data is biased by microstructure noise.
method Uses Queue-Reactive model of limit order book to improve volatility estimation.
result Unified and alternation estimators lead to optimal mean squared error for integrated volatility.
FA-LD algorithm improves uncertainty quantification and mean predictions in federated learning.
problem Uncertainty quantification and mean predictions in federated learning with distributed clients.
method FA-LD algorithm for strongly log-concave distributions with non-i.i.d data, considering general models.
result The FA-LD algorithm provides theoretical guarantees for convergence and optimal noise injection.
A new data-adaptive prior stabilizes kernel learning in operators.
problem Learning kernels in operators from data is ill-posed due to nonlocal dependence.
method Introduces a data-adaptive prior to stabilize the Bayesian posterior mean.
result The data-adaptive prior achieves a stable posterior with small noise limits.
New approach proves convergence of SA and SGD with weaker conditions.
problem Proving convergence of SA and SGD with relaxed noise conditions.
method Introduces GSLLN to decouple function and noise properties.
result Derives sufficient conditions for convergence of SA and SGD.
Deep convolutional neural networks are known to be unstable during training at high learning rate unless normalization techniques are employed. Normalizing weights or activations allows the use of higher learning rates, resulting in faster convergence and higher test accuracy. Batch normalization requires minibatch sta…
Estimates shared linear subspace from noisy data with multiple users.
problem Recovering shared linear subspace from noisy data with non-isotropic noise.
method Estimates shared subspace using at least two data points per user, avoiding restrictive assumptions.
result Upper and lower bounds for estimation error match, showing no additional error due to noise irregularity.
Study duality of zero mean curvature surfaces in Heisenberg group.
problem Understanding the duality of zero mean curvature surfaces in the Lorentzian Heisenberg group.
method Investigation of a transformation surface associated with zero mean curvature surfaces in the Heisenberg group under two metrics.
result Derivation of the Sym formula for the dual surface in both metric cases.
Classifies surfaces with zero mean curvature in a light cone.
problem Classifying surfaces with zero mean curvature in a light cone.
method Examined geodesics and screw motions, used Weierstrass representations.
result Complete classification of ruled zero mean curvature surfaces.
Solves surface problem in 3D light cone.
problem Björling problem for zero mean curvature surfaces in the three-dimensional light cone.
method Solves the Björling problem for zero mean curvature surfaces in the three-dimensional light cone.
result Constructs and classifies all rotational zero mean curvature surfaces.
Study classifies zero mean curvature surfaces with planar curvature lines.
problem Characterizing surfaces with specific curvature properties.
method Complete classification and investigation of their relationship to Thomsen-type surfaces.
result Zero mean curvature surfaces with planar curvature lines belong to a 1-parameter family.
Paper investigates reflection principles for zero mean curvature surfaces in isotropic 3-space.
problem Investigating reflection principles for zero mean curvature surfaces in isotropic 3-space.
method Analyzes reflection principles for zero mean curvature surfaces in I3. result Shows a reflection principle for isotropic line segments on zero mean curvature surfaces in I3. The high-dimensional linear model y=Xβ0+ε is considered and the focus is put on the problem of recovering the support S0 of the sparse vector β0. We introduce Lasso-Zero, a new ℓ1-based estimator whose novelty resides in an "overfit, then threshold" paradigm and the use of noise dictionaries concate…
Modified model prevents volatility from approaching zero.
problem Volatility in the Gatheral model can approach zero, making it statistically indistinguishable.
method Proposed a modified model with Skorokhod reflection to prevent volatility from approaching zero.
result The modified model prevents volatility from approaching zero, preserving the model's flexibility.
Physen-Noise2Noise tackles defocus deblurring in low-light conditions with physics-guided self-supervised learning.
problem Defocus deblurring in low-light conditions with complex biased noise.
method Physics-guided self-supervised deblurring framework that leverages noisy multi-frame observations and a learnable noise bias parameter.
result Physen-Noise2Noise consistently outperforms state-of-the-art methods in defocus deblurring with complex biased noise.
Estimates rank-one spikes from heavy-tailed noise using self-avoiding walks.
problem Estimating rank-one spikes from heavy-tailed noise.
method Self-avoiding walks to count and estimate the spikes.
result Optimal estimation up to the BBP threshold for heavy-tailed noise.
A new gradient estimator for online optimization with two function evaluations.
problem Online optimization of convex and Lipschitz functions with noisy data.
method L1-randomization approach for gradient estimation.
result Compared or better guarantees than previous methods for canceling noise.
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
We propose a dynamic mean field model for `systemic risk' in large financial systems, which we derive from a system of interacting diffusions on the positive half-line with an absorbing boundary at the origin. These diffusions represent the distances-to-default of financial institutions and absorption at zero correspon…
New examples of mixed-type zero-curvature graphs found.
problem Finding new examples of zero-curvature graphs in Lorentz-Minkowski space.
method Using Konderak's representation formula to construct entire zero-curvature graphs over specific planes.
result Existence of new types of entire zero-curvature graphs in mixed-type in Lorentz-Minkowski space.
On any timelike surface with zero mean curvature in the four-dimensional Minkowski space we introduce special geometric (canonical) parameters and prove that the Gauss curvature and the normal curvature of the surface satisfy a system of two natural partial differential equations. Conversely, any two solutions to this …
The paper examines translating solitons and their relation to Lagrangian mean curvature flows with zero Maslov class.
problem Understanding the behavior of Lagrangian translating solitons near Type II singularities.
method Analyzes necessary conditions for blow-up limits and applies to open questions.
result Provides a necessary condition for blow-up limits of Lagrangian mean curvature flows with zero Maslov class.
The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. A major open issue is to verify the presence of LPPL in price sequences and to estimate the LPPL parameters. Estimation is complicated by the fact that daily LPPL returns are typically orders of magnitude smaller than measured price…
Confirmation bias leads to biased estimates in noisy data analysis.
problem Confirmation bias affects scientific conclusions in noisy data environments.
method Investigation of confirmation bias in Gaussian mixture models using K-means and EM algorithms.
result Estimates from algorithms are biased and resemble initial hypotheses, not the noise.
A zero mean curvature surface in the Lorentz-Minkowski 3-space is said to be of Riemann-type if it is foliated by circles and at most countably many straight lines in parallel planes. We classify all zero mean curvature surfaces of Riemann-type according to their causal characters, and as a corollary, we prove that if …
Unbounded convex domains have zero mean curvature on disconnected boundaries.
problem Understanding mean curvature in unbounded convex domains.
method Analyzing mean curvature on disconnected boundary components.
result Mean curvature is zero on disconnected boundary components of unbounded mean convex domains.
It is classically known that the only zero mean curvature entire graphs in the Euclidean 3-space are planes, by Bernstein's theorem. A surface in Lorentz-Minkowski 3-space R13 is called of mixed type if it changes causal type from space-like to time-like. In R13, Osamu Kobayashi found …
New framework for zero mean curvature surfaces in isotropic 3-space.
problem Characterizing zero mean curvature surfaces in isotropic 3-space.
method Introducing ZMC-faces and establishing Osserman-type inequalities.
result Established three Osserman-type inequalities for ZMC-faces.
Deep networks can overfit benignly but still be vulnerable to adversarial attacks.
problem Adversarial vulnerability of deep neural networks trained with benign overfitting.
method Investigated causes of adversarial vulnerability, identified label noise as a key factor, and explored the impact of training procedures and representation learning.
result Adversarial robustness requires more complex decision boundaries than simple ones, suggesting the need for better representation learning.
We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a statistician choosing an estimator -- that is, a measurable function of the observation…
Deep Learning has revolutionized vision via convolutional neural networks (CNNs) and natural language processing via recurrent neural networks (RNNs). However, success stories of Deep Learning with standard feed-forward neural networks (FNNs) are rare. FNNs that perform well are typically shallow and, therefore cannot …
No regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces are found.
problem Existence of regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces.
method Analyzing polynomials defining hypersurfaces of various degrees and shapes.
result Hyperspheres and round cylinders are the only such hypersurfaces defined by polynomials of degree ≤3.
New algorithm reduces MFGs with common noise complexity.
problem Prohibitive computational cost in solving MFGs with common noise.
method Signatured deep fictitious play based on rough path theory.
result Significantly reduced computational complexity and improved efficiency.
Recovering a high-quality image from noisy indirect measurements is an important problem with many applications. For such inverse problems, supervised deep convolutional neural network (CNN)-based denoising methods have shown strong results, but the success of these supervised methods critically depends on the availabi…
Classifies zero mean curvature surfaces in Lorentz-Minkowski space.
problem Classifying surfaces with zero mean curvature.
method Using separable surface equations and constructing examples.
result All zero mean curvature surfaces of separable type have been classified.
Study generalizes matrix completion with side info in low noise settings.
problem Matrix completion with side information in low noise conditions.
method Inductive matrix completion with i.i.d. subgaussian noise, uniform sampling, and side information.
result Generalization bounds with noise scaling, convergence to zero, and logarithmic dependence on matrix size.
Optimal Gaussian noise mechanisms achieve nearly optimal error in unbiased mean estimation.
problem Efficiently estimating the mean of high-dimensional data while preserving privacy.
method Differential privacy mechanisms with Gaussian noise, focusing on optimal covariance.
result Gaussian noise mechanisms achieve nearly optimal error among all private unbiased mean estimation mechanisms.
A new method, Residual-Permuted Sums, improves confidence region construction for linear regression models.
problem Constructing reliable confidence regions for linear regression models with non-symmetric noise.
method Residual-Permuted Sums (RPS) method, which permutes residuals instead of perturbing their signs.
result RPS provides exact finite sample coverage probabilities and is uniformly strongly consistent.