This study evaluates methods for constructing prediction intervals with neural networks.
problem Lack of confidence measures in neural network predictions limits their applicability.
method Two-step experiment using bootstrapping and conformal inference methods.
result Cross-conformal method provides best performance with reasonable computational burden.
SBI provides more accurate pole positions than chi-squared minimization in model misspecification.
problem Accurate pole position estimation in pi-pi scattering models.
method Simulation Based Inference (SBI) method compared to chi-squared minimization.
result SBI leads to more robust predictions of pole positions in models of pi-pi scattering.
Proposes a new cost function for neural networks to improve prediction interval quality.
problem Uncertainty-guided neural network training convergence issues and suboptimal prediction intervals.
method Proposes a customizable smooth cost function for NNs to optimize prediction intervals.
result Significant improvement in prediction interval quality, convergence, and reliability.
HDI-Forest improves regression prediction intervals using Random Forest.
problem Improving the quality of prediction intervals in regression tasks.
method HDI-Forest is a novel quality-based PI estimation method based on Random Forest, optimizing PI quality metrics directly from standard tree-based models.
result HDI-Forest significantly reduces PI width by over 20% compared to previous methods, while maintaining or improving coverage probability.
This paper improves SVM prediction uncertainty quantification methods.
problem Lack of comprehensive UQ methods for SVM predictions.
method Developed SSVQR model for sparse PI estimation and feature selection algorithm.
result Proposed SSVQR model achieves sparse solutions and improves PI quality.
CryptoNAS improves PI accuracy by 3.4% with 2.4x less latency.
problem Private inference on machine learning models with limited latency.
method Developed CryptoNAS, a novel NAS method for finding models that maximize accuracy within a ReLU budget.
result Improves accuracy by 3.4% and latency by 2.4x over state-of-the-art methods.
This paper presents a method to automatically generate high-quality prediction intervals for neural networks.
problem Accurate uncertainty quantification for deep learning models in real-world applications.
method Dual neural network approach with a novel loss function to balance prediction interval width and coverage.
result Our method produces significantly narrower prediction intervals with higher probability coverage compared to state-of-the-art methods.
New research suggests privileged information doesn't improve model performance.
problem Challenges in transferring knowledge using privileged information in machine learning.
method Critical examination of existing theoretical and empirical analyses of LUPI methods.
result LUPI methods often fail to effectively transfer knowledge from privileged information.
Proposes a method to generate prediction intervals using weighted asymmetric loss functions.
problem Generating reliable prediction intervals for neural network models.
method Uses a weighted asymmetric loss function to estimate prediction intervals.
result The method produces reliable prediction intervals in complex machine learning scenarios.
Paper proves PI consensus algorithm converges exponentially under restricted secant inequality.
problem Proving convergence of PI consensus algorithm without convexity.
method Lyapunov theory, restricted secant inequality, rate-matching discretization, local pre-conditioning.
result Exponential convergence of PI consensus algorithm for non-convex functions.
pi-VAE models neural activity with interpretable latent variables.
problem Difficult interpretation of deep generative models for neural data.
method Adapted variational auto-encoder to integrate task variables.
result Improves interpretability and identifiability of neural codes.
We show that the triangle with angles Pi/12, Pi/3 and 7*Pi/12 has the lattice property and compute this triangle's Veech group.
Adaptive PI by reweighting nonconformity scores improves model uncertainty reflection.
problem CP methods using a constant correction for all test points ignore individual uncertainties.
method QRF learns distribution of nonconformity scores and assigns weights to samples.
result PI lengths more aligned with model uncertainty and improved adaptiveness.
PIF detects anomalies in structured patterns using preference embedding.
problem Detecting anomalies with respect to structured patterns.
method PIF combines adaptive isolation methods with preference embedding to compute anomaly scores using a tree-based method, PI-Forest.
result PIF outperforms state-of-the-art techniques in anomaly detection.
Paper improves neural network uncertainty quantification.
problem Generating narrow yet reliable prediction intervals for deep learning models.
method Derives a loss function from an axiom of uncertainty quantification, uses gradient descent, and ensembles model uncertainty.
result Significantly reduces prediction interval width compared to existing methods.
Proposes PI-VAE for solving SDEs with limited measurements.
problem Solving SDEs with limited measurements of system parameters.
method Physics-informed Variational Autoencoder (PI-VAE) integrating VAE and governing equations.
result Satisfactory accuracy and efficiency compared to PI-WGAN.
Every torus knot can be represented as a Fourier-(1,1,2) knot which is the simplest possible Fourier representation for such a knot. This answers a question of Kauffman and confirms the conjecture made by Boocher, Daigle, Hoste and Zheng. In particular, the torus knot T(p,q) can be parameterized as x(t)=cos(pt), y(t)=c…
Modified SPSNN reduces Pi nodes using adaptive multinomial choice.
problem Reduce the number of Pi nodes in SPSNNs.
method Adaptive approach to find better multinomial for a given problem.
result MSPSNN behaves better than traditional SPSNN with P_s.
Let K be a knot of genus g. If K is fibered, then it is well known that the knot group pi(K) splits only over a free group of rank 2g. We show that if K is not fibered, then pi(K) splits over non-free groups of arbitrarily large rank. Furthermore, if K is not fibered, then pi(K) splits over every free group of rank at …
Lower bounds for PI on multi-action MDPs are established, showing complexity grows with action count.
problem Establishing the minimum number of iterations for PI to converge on MDPs with multiple actions.
method Developed lower bounds for a specific PI variant on multi-action MDPs, scaling with action count.
result A particular PI variant can take Ω(kn/2) iterations to terminate, scaling with action count. A framework to explain decoder-only sequence classification models using intermediate predictions.
problem Explaining predictions of decoder-only sequence classification models.
method Progressive Inference framework with Single Pass-Progressive Inference and Multi Pass-Progressive Inference methods.
result Significantly better attributions compared to prior work on text classification tasks.
A K(pi,1)-foliation is one for which the universal covers of all leaves are contractible (thus all leaves are K(pi,1)'s for some pi). In the first part of the paper we show that the tangential Lusternik--Schnirelmann category cat F of a K(pi,1)-foliation F on a manifold M is bounded from below by t-codim F for any t wi…
Physics-informed GCRL tackles sparse feedback learning with hybrid dynamics.
problem Sparse feedback learning with high-dimensional, hybrid, or contact-dependent dynamics.
method Introduces physics-informed inductive biases into goal-conditioned value learning.
result Contact-rich manipulation tasks degrade existing Pi-GCRL methods.
New Ricci curvature means derived from plane curvatures.
problem Understanding Ricci curvature in geometric contexts.
method Introducing intrinsic and normal mean Ricci curvatures via Jacobi-field expansions and applying Bochner-Weitzenboeck identity.
result Derives a Bochner-Weitzenboeck identity for simple d-vectors.
Gromov and Lawson conjectured that a closed spin manifold M of dimension n with fundamental group pi admits a metric with positive scalar curvature if and only if an associated element in KO_n(B pi) vanishes. In this note we present counter examples to the `if' part of this conjecture for groups pi which are torsion fr…
PIED optimizes experimental design for inverse problems using physics-informed neural networks.
problem Optimizing experimental design for inverse problems with limited budget and constraints.
method PIED uses physics-informed neural networks (PINNs) for continuous optimization of design parameters in one-shot deployments.
result PIED significantly outperforms existing ED methods in solving inverse problems, including unknown functions.
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a dataset. A useful re…
PI-SAC agents learn predictive information to improve RL efficiency.
problem Improving sample efficiency in reinforcement learning.
method PI-SAC agents use a contrastive version of Conditional Entropy Bottleneck to learn predictive information from past and future states.
result PI-SAC agents significantly improve sample efficiency on challenging continuous control tasks.
In this article we construct a minimal symplectic 4-manifold R that has small Euler characteristic (e(R)=8) and two essential Lagrangian tori with nice properties. These properties make R particularly suitable for constructing interesting examples of symplectic manifolds with small Euler characteristic. In particular, …
Given a closed manifold N and a self-indexing Morse function f: N --> R with up to four distinct Morse indices, we construct a symplectic Lefschetz fibration pi: E --> C which models the complexification of f on the disk cotangent bundle, f_C : D(T*N) --> C, when f is real analytic. By construction, pi: E --> C comes w…
TQA improves prediction intervals for time series data by adjusting quantiles for both cross-sectional and longitudinal coverage.
problem Constructing reliable prediction intervals for cross-sectional time series data.
method Temporal Quantile Adjustment (TQA) method that adjusts the quantile in Conformal Prediction to account for both cross-sectional and longitudinal coverage.
result TQA improves longitudinal coverage while preserving cross-sectional coverage, as validated through extensive experimentation.
New method predicts aphasia severity with narrower uncertainty intervals.
problem Predicting aphasia severity in stroke patients using neuroimages.
method Sparse heteroscedastic Bayesian high-dimensional regression with H-PROBE algorithm.
result H-PROBE provides narrower prediction intervals for aphasia severity.
Let pi be a free group of rank 2. Its outer automorphism group Out(pi) acts on the space of equivalence classes of representations in Hom(pi, SL(2,C)). Let SLm(2,R) denote ths subset of GL(2,R) consisting of matrices of determinant -1 and let ISL(2,R) denote the subgroup (SL(2,R) union i SLm(2,R)) of SL(2,C). The repre…
New algorithms explain Naive Bayes classifiers in polynomial time and delay.
problem Computing explanations for Naive Bayes classifiers efficiently.
method Developed log-linear time and polynomial delay algorithms for PI-explanations.
result Efficiently computed PI-explanations for linear classifiers.
Infinite rank groups found in 3-manifolds with infinite fundamental groups.
problem Understanding the structure of diffeomorphism and homeomorphism groups of 3-manifolds with infinite fundamental groups.
method Analyzing actions of barbell diffeomorphisms on spaces of embedded arcs and configuration spaces.
result Groups of diffeomorphisms and homeomorphisms have infinite rank.
Given k>=2, we construct a (2k-2)-parameter family of properly embedded minimal surfaces in H^2 x R invariant by a vertical translation T, called Saddle Towers, which have total intrinsic curvature 4 pi(1-k), genus zero and 2k vertical Scherk-type ends in the quotient by T. As limits of those Saddle Towers, we obtain J…
SCI-PI solves scale invariant problems efficiently.
problem Solving scale invariant problems in optimization.
method Introduces SCI-PI and proves its convergence.
result SCI-PI achieves local linear convergence.
SPI-Optimizer separates momentum term to eliminate oscillation in stochastic optimization.
problem Oscillation in momentum-based optimizers.
method Integrates conditional integration from classical control theory to separate momentum term.
result Significantly reduces oscillation and improves convergence speed and accuracy.
We show that many 3-manifold groups have no nonabelian surface subgroups. For example, any link of an isolated complex surface singularity has this property. In fact, we determine the exact class of closed graph-manifolds which have no immersed pi_1-injective surface of negative Euler characteristic. We also determine …
Let S be a closed, oriented surface of genus at least 2, and consider the extension 1 -> pi_1 S -> MCG(S,p) -> MCG(S) -> 1, where MCG(S) is the mapping class group of S, and MCG(S,p) is the mapping class group of S punctured at p. We prove that any quasi-isometry of MCG(S,p) which coarsely respects the cosets of the no…
New visual tools show feature importance for black box models.
problem Improving transparency and trust in machine learning models.
method Local feature importance, PI and ICI plots, partial dependence, individual conditional expectation.
result Visual tools accurately represent feature importance for black box models.
Let Pi: M -> B be an onto maximal rank map or a Riemannian submersion between Riemannian manifolds M and B. Initially, we prove necessary and sufficient conditions for any fiber F to be roughly isometric to M. Then, we prove necessary and sufficient conditions for Pi to be a rough isometry. As a corollary M is roughly …
SEF method generates prediction intervals by shifting error function in neural networks.
problem Quantifying uncertainty in neural network predictions.
method Training a neural network three times to generate upper and lower bounds, using a parameter from initial estimates.
result SEF method effectively produces prediction intervals, outperforming other methods in evaluations.
Given any knot k, there exists a hyperbolic knot tilde k with arbitrarily large volume such that the knot group pi k is a quotient of pi tilde k by a map that sends meridian to meridian and longitude to longitude. The knot tilde k can be chosen to be ribbon concordant to k and also to have the same Alexander invariant …
In this note we prove that a complex hyperbolic triangle group of type (m,m,infinity), i.e. a group of isometries of the complex hyperbolic plane, generated by complex reflections in three complex geodesics meeting at angles Pi/m, Pi/m and 0, is not discrete if the product of the three generators is regular elliptic.
Given a closed orientable Euclidean cone 3-manifold C with cone angles less than or equal to pi, and which is not almost product, we describe the space of constant curvature cone structures on C with cone angles less than pi. We establish a regeneration result for such Euclidean cone manifolds into spherical or hyperbo…
SINDy-PI robustly identifies implicit dynamics from noisy data.
problem Accurately modeling nonlinear dynamics from noisy data.
method Parallel, implicit SINDy algorithm with multiple optimization algorithms and model selection.
result Significantly more noise robust than previous SINDy approaches.
This paper gives necessary and sufficient conditions on a compact, connected, orientable 3-manifold M for it to contain a knot K such that M-K is irreducible and pi_1(M) embeds in pi_1(M-K). This result provides counterexamples to a conjecture of Lopes and Morales and characterizes those orientable 3-manifolds for whic…