Enhances Cox model for survival analysis with symbolic non-linear log-risk functions.
problem Limited interpretability and non-linearity in traditional Cox models.
method Introduces GCPH model using Kolmogorov-Arnold Networks for symbolic non-linear log-risk functions.
result GCPH achieves competitive performance and superior interpretability.
Paper presents a fast framework for root cause analysis in large-scale systems.
problem Challenges in reviewing logs for identifying issues in large-scale production environments.
method Automates root cause analysis on structured logs with improved scalability using frequent item-set mining and association rule learning.
result Proposes a framework that selects unique item-sets for target failures, improving interpretability and scalability.
Develops pathwise analysis for log-optimal portfolios using rough paths theory.
problem Analyzing stability and approximation of log-optimal portfolios.
method Pathwise approach based on càdlàg rough paths theory.
result Establishes pathwise stability and error estimates for log-optimal portfolios.
The main task in oil and gas exploration is to gain an understanding of the distribution and nature of rocks and fluids in the subsurface. Well logs are records of petro-physical data acquired along a borehole, providing direct information about what is in the subsurface. The data collected by logging wells can have si…
The paper proposes a new method for clustering survival data using smoothed log-hazard trajectories.
problem Clustering survival data based on instantaneous risk dynamics.
method Functional Principal Component Analysis applied to B-spline smoothed log-hazard trajectories.
result The proposed method provides an interpretable representation of relative temporal risk dynamics.
Study on policy gradient for stochastic bandits using diffusion approximation.
problem Improving policy gradient methods for stochastic bandits with optimal regret bounds.
method Continuous-time diffusion approximation of policy gradient with learning rate analysis.
result Proved optimal regret bound of O ( k log ( k ) log ( n ) / η ) O(k \log(k) \log(n) / η) O ( k log ( k ) log ( n ) / η ) for η = O ( Δ 2 / log ( n ) ) η= O(Δ^2/\log(n)) η = O ( Δ 2 / log ( n )) . LMC achieves sqrt(d) dependence in sampling error, improving previous bounds.
problem Analyzing sampling error in Langevin Monte Carlo.
method Refined mean-square analysis for discretizations of contractive SDEs.
result Establishes i l d e O ( d / ε ) ilde{O}(\sqrt{d}/ε) i l d e O ( d / ε ) mixing time bound for LMC. Improved convergence for non-log-concave sampling.
problem Sampling from non-log-concave distributions.
method Novel conductance analysis of SGLD with auxiliary Markov Chain.
result SGLD achieves ε-sampling error with fewer evaluations.
CAVI converges for log-concave measures via optimal transport.
problem Finding the closest product measure to a log-concave measure via CAVI.
method Adapting coordinate descent techniques from Euclidean space to optimal transport for log-concave densities.
result Proves convergence of CAVI for log-concave densities and provides rates of convergence under additional conditions.
Deep learning models detect and classify log anomalies.
problem Anomaly detection in unstructured log data.
method Auto-LSTM, Auto-BLSTM, and Auto-GRU models for feature extraction.
result Models outperform other algorithms on various log data sets.
This paper extends compositional data analysis using graph signal processing.
problem Traditional log-ratios between all variables are not suitable for specific variable relationships.
method Linking compositional data analysis with graph signal processing, it considers only selected log-ratios.
result The approach retains desirable properties of scale invariance and compositional coherence.
Recent studies have found that the log-volatility of asset returns exhibit roughness. This study investigates roughness or the anti-persistence of Bitcoin volatility. Using the multifractal detrended fluctuation analysis, we obtain the generalized Hurst exponent of the log-volatility increments and find that the genera…
Differentially private log-location-scale regression models improve privacy in statistical analysis.
problem Ensuring privacy in statistical regression models while maintaining accuracy.
method Integrates differential privacy into LLS regression using the functional mechanism.
result Proposed DP-LLS models satisfy ε-differential privacy and perform well under various conditions.
Improved sampling guarantees for weakly log-concave distributions.
problem Sampling from distributions that are not strongly log-concave.
method Proximal sampler with convergence guarantees under weaker assumptions.
result New state-of-the-art sampling guarantees for various target distributions.
Paper analyzes statistical properties of log-cosh loss function.
problem No statistical analysis of log-cosh loss function in literature.
method Presented statistical properties of log-cosh loss function, compared to Cauchy distribution, and examined various statistical procedures.
result Characterized statistical properties of log-cosh loss function, including distribution, likelihood function, and Fisher information.
In this article, we mathematically study several GAN related topics, including Inception score, label smoothing, gradient vanishing and the -log(D(x)) alternative. --- An advanced version is included in arXiv:1703.02000 "Activation Maximization Generative Adversarial Nets". Please refer Section 6 in 1703.02000 for deta…
Non-Gaussian component analysis (NGCA) is aimed at identifying a linear subspace such that the projected data follows a non-Gaussian distribution. In this paper, we propose a novel NGCA algorithm based on log-density gradient estimation. Unlike existing methods, the proposed NGCA algorithm identifies the linear subspac…
New ANN method for imputing rounded zeros in compositional data.
problem Imputing missing values in compositional data with rounded zeros.
method Artificial Neural Networks (ANNs) for imputation of compositional data.
result ANNs are competitive or better than conventional methods for imputing rounded zeros.
PACMAN provides bounds for classification tasks considering accuracy vs. negative log-loss mismatch.
problem Mismatch between accuracy and negative log-loss in classification tasks.
method Point-wise PAC approach over generalization gap, using likelihood ratio and concentration inequalities.
result PACMAN provides point-wise PAC bounds for the generalization problem.
Study tests rough fractional volatility model across different time scales, revealing new volatility patterns.
problem Testing robustness of rough fractional volatility model over various time scales.
method Used large dataset on FX rates, included smoothing and measurement errors, analyzed log-log plots of realized variance increments.
result Found new stylized facts in volatility patterns, including convexity and nonlinear behavior.
We study the linear contextual bandit problem with finite action sets. When the problem dimension is d d d , the time horizon is T T T , and there are n ≤ 2 d / 2 n \leq 2^{d/2} n ≤ 2 d /2 candidate actions per time period, we (1) show that the minimax expected regret is Ω ( d T ( log T ) ( log n ) ) Ω(\sqrt{dT (\log T) (\log n)}) Ω ( d T ( log T ) ( log n ) ) for every algorithm, and (2) introduce a V…
Improves SGM convergence bounds in W2-distance without strict assumptions.
problem Convergence bounds for SGMs in W2-distance require stringent assumptions.
method Novel framework using the OU process and PDE analysis.
result Log-concavity evolves from weak to strong over time.
The paper assesses dimensionality reduction for cryptocurrency link prediction.
problem Establishing a link between cryptocurrencies using dimensionality reduction techniques.
method Used canonical correlation analysis and principal component analysis on log returns and covariates of Bitcoin and Ethereum.
result Performance of dimensionality reduction techniques in forecasting Ethereum returns with Bitcoin features.
Study compares Bitcoin, gold, and gas price complexity using multifractal and multiscale entropy methods.
problem Quantifying complexity of financial time series for market analysis.
method Employed MF-DFA and RCMSE to analyze Bitcoin, GBP/USD, gold, and natural gas price log-return time series.
result Bitcoin shows higher complexity compared to other markets, linked to higher nonlinear correlations.
New analysis of signSGD with random reshuffling shows faster convergence rates.
problem Understanding the convergence of signSGD with random reshuffling in nonconvex optimization.
method Developed new sign-based algorithms (SignRVR, SignRVM) and analyzed convergence rates.
result Achieved faster convergence rates for signSGD with random reshuffling.
Study identifies Kähler-Einstein, Kähler-Ricci soliton, and Sasaki-Einstein metrics on log del Pezzo surfaces.
problem Characterizing log del Pezzo surfaces with specific geometric properties.
method Examining two classes of non-toric log del Pezzo surfaces and analyzing their geometric properties.
result Examples found that admit Kähler-Ricci solitons but not Sasaki-Einstein cone links.
The Restricted Boltzmann Machines (RBM) can be used either as classifiers or as generative models. The quality of the generative RBM is measured through the average log-likelihood on test data. Due to the high computational complexity of evaluating the partition function, exact calculation of test log-likelihood is ver…
Corrected graph convolutions improve node classification on graphs.
problem Oversmoothing in graph convolutions degrades performance.
method Theoretical analysis based on CSBM, spectral analysis for k rounds of corrected graph convolutions.
result Corrected graph convolutions can improve node classification performance exponentially.
Log-ergodic model improves velocity of money prediction.
problem Improving velocity of money prediction for economic control.
method Log-ergodic processes to simulate monetary velocity.
result Log-ergodic model offers superior predictive power.
Deep signature/log-signature FBSDE algorithm improves accuracy and training time.
problem Solving FBSDEs with state and path dependent features.
method Incorporates deep signature/log-signature transformation into RNN model.
result Improves accuracy and training time compared to existing methods.
GN algorithm solves batched bandit for nondegenerate functions near-optimally.
problem Batched bandit learning for nondegenerate functions.
method Introduces Geometric Narrowing (GN) algorithm with a O ~ ( A + d T ) \widetilde{\mathcal{O}} ( A_{+}^d \sqrt{T} ) O ( A + d T ) regret bound and O ( log log T ) \mathcal{O} (\log \log T) O ( log log T ) batches. result GN achieves near optimal regret with minimal number of batches.
Improved sampling guarantees for underdamped Langevin Monte Carlo without restrictive assumptions.
problem Sampling from unnormalized densities with improved guarantees and acceleration.
method Novel analysis relaxing assumptions on log-Sobolev inequality and Hessian smoothness, using Rényi discretization bounds.
result First KL divergence guarantees for ULMC without Hessian smoothness under strong log-concavity.
ResNets approximate log-Gaussian at initialization, improving network performance.
problem Understanding the initialization behavior of deep neural networks like ResNets.
method Analyzing ReLU ResNets in the infinite-depth-and-width limit, showing log-Gaussian behavior.
result ResNets at initialization exhibit hypoactivation and interlayer correlations, which are not captured by Gaussian limits.
This study was conducted to find an appropriate statistical model to forecast the volatilities of PSEi using the model Generalized Autoregressive Conditional Heteroskedasticity (GARCH). Using the R software, the log returns of PSEi is modeled using various ARIMA models and with the presence of heteroskedasticity, the l…
We propose that imitation between traders and their herding behaviour not only lead to speculative bubbles with accelerating over-valuations of financial markets possibly followed by crashes, but also to ``anti-bubbles'' with decelerating market devaluations following all-time highs. For this, we propose a simple marke…
Improved KLMC for sampling under various conditions.
problem Stable simulation of kinetic Langevin dynamics under different parameters.
method Revisited synchronous Wasserstein coupling analysis with stochastic exponential Euler discretization.
result Exponential integrator can simulate kinetic Langevin dynamics in the overdamped regime with proper time acceleration.
The paper develops methods for sampling from log-concave distributions with constraints.
problem Sampling from log-concave distributions with constraints.
method Randomized midpoint discretization of Langevin diffusions with various projections.
result New convergence guarantees for constrained Langevin algorithms.
New framework predicts AMP behavior in spiked models for finite iterations.
problem Understanding AMP dynamics in high-dimensional spiked models.
method Developed a non-asymptotic framework for AMP in spiked matrix estimation.
result Predicted AMP behavior for up to O ( n p o l y log n ) O\big(\frac{n}{\mathrm{poly}\log n}\big) O ( poly l o g n n ) iterations in Z 2 \mathbb{Z}_2 Z 2 synchronization. The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly convex minimization problems. Typical applications include many popular statistical…
Improved Langevin algorithms with prior diffusion achieve dimension-independent convergence for non-log-concave distributions.
problem Understanding the dimension dependency of computational complexity in high-dimensional sampling.
method Investigation of prior diffusion technique for log-Sobolev inequality target distributions.
result Modified Langevin algorithm achieves dimension-independent KL divergence convergence.
LMC algorithm receives first convergence guarantees under weak smoothness conditions.
problem Convergence guarantees for LMC under weak smoothness conditions.
method Using Latała--Oleszkiewicz or modified log-Sobolev inequalities.
result First convergence guarantees for LMC under weak smoothness conditions.
SurvMixClust clusters survival data and predicts individual survival curves.
problem Integrating clustering into survival analysis for precision medicine.
method SurvMixClust learns latent representations for clustering and predicts survival functions using a mixture of non-parametric experts.
result SurvMixClust creates balanced clusters with distinct survival curves, outperforming clustering baselines and competing with non-clustering models in predictive accuracy.
The analysis of nonconvex matrix completion has recently attracted much attention in the community of machine learning thanks to its computational convenience. Existing analysis on this problem, however, usually relies on ℓ 2 , ∞ \ell_{2,\infty} ℓ 2 , ∞ projection or regularization that involves unknown model parameters, although th…
Unified analysis of multi-attribute graph learning with non-convex penalties.
problem Graph inference from multi-attribute data.
method Penalized log-likelihood objective function with ADMM and local linear approximation.
result Local consistency in support recovery and precision matrix estimation for non-convex penalties.
New method reduces regret and communication costs in federated Q-learning.
problem Worst-case regret and communication cost bounds in federated Q-learning.
method Gap-dependent analysis leveraging MDP structures.
result Achieves log T \log T log T -type regret and communication cost bounds. Paper presents a new method to detect process differences at the trace level using mutual fingerprints.
problem Low-level granularity in process variant analysis leads to many false differences.
method Develops a mutual fingerprint technique to encode entire process traces for comparison.
result Mutual fingerprint method reveals significant differences not detected by existing techniques.
Study on online regression with noise, achieving near-optimal regret bounds.
problem Online generalized linear regression with stochastic noise.
method Sharp analysis of FTRL algorithm for stochastic label noise.
result Achieved near-optimal regret bounds for O ( σ 2 d log T ) + o ( log T ) O(σ^2 d \log T) + o(\log T) O ( σ 2 d log T ) + o ( log T ) . TDA detects financial bubbles through early warning signals.
problem Detecting financial bubbles early.
method Using Log-Periodic Power Law Singularity (LPPLS) model to fit financial time series data.
result TDA generates early warning signals when LPPLS model fits the data.