The study analyzes gaps in well logs to improve prediction models.
problem Improving prediction of missing data in well logs for oil exploration.
method Descriptive analysis, generation of artificial gaps, comparison of machine learning algorithms.
result Artificial Neural Networks, Random Forests, and Linear Regression algorithms were compared in predicting missing data.
Constructs curves in log-symplectic manifolds, classifying and obstructing certain structures.
problem Classifying and understanding curves in log-symplectic manifolds.
method Constructs moduli spaces of curves, uses symplectic field theory.
result Classifies symplectically ruled log-symplectic 4-manifolds, obstructs contact boundary components.
Corrects pseudo log-likelihood method issues in various applications.
problem Log-likelihood function unbounded issues in pseudo log-likelihood methods.
method Provided a counterexample and corrected algorithms in previous literature.
result Ensured well-definedness of maximum pseudo log-likelihood estimation.
EnLSTM network improves log generation from small datasets.
problem Generating well logs from small datasets with high accuracy.
method Combining ENN and C-LSTM networks with perturbation methods.
result 34% reduction in mean-square-error compared to existing models.
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.
Novel multiclass SVM framework classifies lithology from well logs.
problem Classifying lithology types from well logs.
method Multiclass SVM approach using one-against-all strategy.
result Multiclass SVM outperforms other classifiers in classification accuracy.
Study on sequential prediction with log-loss, focusing on well-specified and misspecified cases.
problem Sequential prediction with log-loss under different specification conditions.
method Analysis of cumulative regret in well-specified and misspecified cases for a Gaussian location hypothesis class.
result Cumulative regrets in well-specified and misspecified cases asymptotically coincide for the d d d -dimensional Gaussian location hypothesis class. We present a method for constructing the log-optimal portfolio using the well-calibrated forecasts of market values. Dawid's notion of calibration and the Blackwell approachability theorem are used for computing well-calibrated forecasts. We select a portfolio using this "artificial" probability distribution of market …
This work improves neural network calibration using explicit regularization.
problem Improving predictive uncertainty in neural networks.
method Introducing a probabilistic calibration measure and exploring explicit regularization techniques.
result Explicit regularization improves log-likelihood and predictive uncertainty.
Paper characterizes log-optimal portfolio without NFLVR assumption.
problem Characterizing log-optimal portfolio in models violating NFLVR.
method Complete characterization of log-optimal portfolio and its deflator without NFLVR.
result Necessary and sufficient conditions for the existence of log-optimal portfolio and its deflator are provided.
The study proves a theorem about subword complexity for free group automorphisms.
problem Analyzing subword complexity for attracting fixed points of automorphisms of free groups.
method Combinatorial arguments and train tracks.
result Subword complexity of attracting fixed points is equivalent to n, n log log n, n log n, or n^2.
New lower bounds for sampling from log-concave distributions in higher dimensions.
problem Proving lower bounds for sampling from log-concave distributions in higher dimensions.
method Multiscale construction inspired by geometric measure theory and reduction to block Krylov algorithms.
result Query lower bounds for sampling from log-concave distributions in higher dimensions are established.
New insights from centro-affine geometry solve a key geometric conjecture.
problem Log-Brunn-Minkowski conjecture in centro-affine differential geometry.
method Interpreting the log-Brunn-Minkowski conjecture as a spectral problem and using centro-affine differential geometry.
result Global uniqueness and inequalities in the log-Minkowski problem for certain convex bodies.
Model monthly VIX and stock returns using log-Heston model.
problem Modeling monthly VIX and stock index returns accurately.
method Log-Heston model applied to logarithm of VIX as an autoregression, normalizing stock returns by VIX.
result Model captures independent, identically distributed Gaussian stock returns after normalization.
Proposes a differentiable LSE-ICNN for modeling multi-well potentials.
problem Modeling multi-well potentials in various scientific domains.
method Log-sum-exponential (LSE) mixture of input convex neural network (ICNN) modes.
result Smooth surrogate that retains convexity within basins and allows gradient-based learning.
This paper shows how to approximate any log-concave distribution using well-conditioned affine coupling flows.
problem Understanding the representational power of affine coupling flows for log-concave distributions.
method Leveraging connections between affine coupling architectures, Langevin dynamics, and Hénon maps to prove log-concave approximation.
result Any log-concave distribution can be approximated using well-conditioned affine-coupling flows.
Extends OPE to evaluate policies using diverse logging data.
problem Evaluate policies using log data from different policies.
method Develops an OPE method for various logging policies.
result Method's predictions converge to true performance as sample size increases.
SplineCalib calibrates probabilities using splines for better performance.
problem Calibrating probabilities for better accuracy and log-loss.
method Uses smoothing splines to determine a calibration function.
result Significant improvements to log-loss and accuracy on various problems.
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.
Model non-stationary financial data using log-normal distributions and Langevin equations.
problem Modeling non-stationary volume-price distributions in finance.
method Model non-stationary volume-price distributions with a log-normal distribution. Derive Langevin equations from the series of log-normal parameters.
result Reconstructed statistics of volume-price distributions fit well empirical data.
Paper explores alternatives to softmax loss for classification.
problem Unclear why log-softmax performs better than alternatives.
method Investigated spherical family loss functions for classification.
result Spherical alternatives outperform log-softmax on MNIST and CIFAR-10.
New SLC distributions enable easier control over diversity.
problem Lack of easy control over diversity in existing models.
method Developed strongly log-concave distributions and two tools for sampling and mode finding.
result Established weak log-submodularity for SLC functions and optimization guarantees for mode finding.
Paper presents efficient algorithms for robust PCA with reduced computational complexity.
problem Robust PCA in fully and partially observed settings, especially when corruptions are present.
method Non-convex optimization approach using gradient descent.
result Significant reduction in computational complexity compared to existing algorithms.
Improved Gaussian process regression with tighter log marginal likelihood bounds.
problem Improving predictive performance in Gaussian process regression models.
method Lower bound on log marginal likelihood using conjugate gradients.
result Improved predictive performance compared to other conjugate gradient based approaches.
In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in R 2 . \Bbb R^2. R 2 . The classification gives some interesting phenomena and consequences including: the family of curves conv…
Randomized graph construction ensures giant component with fewer edges.
problem Efficiently constructing sparse graphs with good connectivity.
method Randomly connecting points to a subset of their nearest neighbors.
result A sparser graph with comparable connectivity properties.
This paper introduces a method to estimate log-likelihood in VAE models.
problem Difficulty in comparing models trained via ELBO due to lack of log-likelihood.
method Introduces a general upper bound to approximate model evidence.
result Efficiently approximates model evidence and compares to other bounds.
Boosted decision trees typically yield good accuracy, precision, and ROC area. However, because the outputs from boosting are not well calibrated posterior probabilities, boosting yields poor squared error and cross-entropy. We empirically demonstrate why AdaBoost predicts distorted probabilities and examine three cali…
By using a coupling method, an explicit log-Harnack inequality with local geometry quantities is established for (sub-Markovian) diffusion semigroups on a Riemannian manifold (possibly with boundary). This inequality as well as the consequent L 2 L^2 L 2 -gradient inequality, are proved to be equivalent to the pointwise curva…
Improves latent variable use in generative models.
problem Poor use of latent variables in variational autoencoders (VAEs).
method Combines data log likelihood with autoencoder reconstruction likelihood.
result Ensures latent variable captures observation information and generates well.
Thresholded Lasso bandit minimizes regret in sparse linear bandits.
problem Sparse stochastic contextual linear bandits with large feature vectors.
method Uses Lasso framework with thresholding to estimate reward function and its sparse support.
result Non-asymptotic regret upper bounds scaling as O ( log d + T ) \mathcal{O}( \log d + \sqrt{T}) O ( log d + T ) . A phenomenon of the financial log-periodicity is discussed and the characteristics that amplify its predictive potential are elaborated. The principal one is self-similarity that obeys across all the time scales. Furthermore the same preferred scaling factor appears to provide the most consistent description of the mar…
The paper proves complex Monge-Ampère equations with new singularity types and confirms log-concavity of volume.
problem Existence and uniqueness of solutions to complex Monge-Ampère equations with prescribed singularities.
method Proves existence and uniqueness of solutions to complex Monge-Ampère equations with general model type singularities in big cohomology classes.
result Log-concavity of volume of closed positive (1,1)-currents is confirmed.
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.
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.
Study shows CNNs can perform well with less data using biological synaptic distributions.
problem Training deep neural networks with limited data.
method Synthesizing CNNs using log-normal or correlated center-surround synaptic strength distributions.
result CNNs with biological synaptic strength distributions can perform well with fewer data samples.
Critical volatility triggers log-normal to power-law transitions in interconnected systems.
problem Understanding the transition from log-normal to power-law distributions in interconnected systems.
method Analyzing an infinite option-on-option chain model, deriving a critical volatility threshold.
result A critical volatility threshold of approximately 250.66% for unconditional cases, dropping to 125.3% with selective survival.
Study online monotone density estimation with expert aggregation and log-optimal calibration.
problem Online monotone density estimation and log-optimal calibration.
method Proposed two online estimators: Grenander estimator and expert aggregation estimator.
result Online estimators achieve O ( n 1 / 3 ) O(n^{1/3}) O ( n 1/3 ) cumulative log-likelihood gap and n log n \sqrt{n\log{n}} n log n pathwise regret bound. The paper proves the existence of Sasaki-Einstein metrics on specific Sasakian manifolds.
problem Proving the existence of conic Sasaki-Einstein metrics on log Fano Sasakian manifolds of dimension five.
method Deriving uniform L^{4}-bounds and analyzing the conic Sasaki-Ricci flow.
result Existence of conic Sasaki-Einstein metrics on log Fano Sasakian manifolds of dimension five.
Introduces new weighted floating functions and affine surface areas.
problem Developing new mathematical concepts for convex bodies.
method Introducing weighted floating functions and weighted functional affine surface areas.
result New relations to traditional and classical affine surface areas.
New deficit functions link elliptic and parabolic inequalities, proving log Sobolev.
problem Proving log Sobolev inequality using deficit functions.
method Introducing two deficit functions, one elliptic and one parabolic, and showing their pointwise convergence and equations.
result Elliptic deficit converges to parabolic deficit, leading to an elliptic proof of log Sobolev inequality.
Separable losses are inconsistent for structured prediction models.
problem Inconsistency of separable losses in structured prediction models.
method Analysis of separable negative log-likelihood losses for structured prediction.
result Separable losses are not Bayes consistent and may not predict the most probable structure.
Data science predicts user interest for midwifery content.
problem Improving midwives' learning and preventing maternal and newborn deaths.
method Forecasting methods using user-generated logs from online learning apps.
result Determining future user interest in midwifery content types.
Bounds on long-term returns of leveraged ETFs are given.
problem Uncertainty in long-term returns of leveraged ETFs.
method Quadratic bounds on log-returns based on daily log-returns of the underlying index.
result Sufficient conditions for outperformance and underperformance of leveraged ETFs.
A new HMC method reduces variance for sampling from smooth, log-concave distributions.
problem Sampling from smooth, log-concave distributions efficiently.
method Stochastic Hamilton Monte Carlo with variance reduction.
result Achieves improved gradient complexity for accuracy.
Proves error bounds for PGD, extending log-Sobolev and Talagrand inequalities.
problem Maximum likelihood estimation of large latent variable models.
method Extending log-Sobolev and Talagrand inequalities to models with strongly concave log-likelihoods.
result Non-asymptotic error bounds for PGD in models satisfying LSI and PŁI.
New clustering technique improves RNN event log predictions.
problem Leveraging event attributes for better RNN predictions.
method A novel clustering technique for event attributes.
result Improved prediction accuracy with reduced training time.
A new method normalizes EBM training by introducing a learnable parameter.
problem Training energy-based models with maximum likelihood is challenging due to intractable normalisation constants.
method Proposes a self-normalised log-likelihood (SNL) objective that introduces a learnable parameter representing the normalisation constant.
result The SNL objective is a lower bound of the log-likelihood and can be directly optimised using stochastic gradient techniques.