New method finds exponential growth in knot types from sticks.
problem How many knots can be formed with a fixed number of sticks?
method Polygonal self-intersection to sparse real-algebraic chamber problem, braid construction.
result Factorial-scale upper bound for knot types, optimal growth order.
Study subgroup growth in RAAGs and RAAGs with Coxeter relations.
problem Understanding subgroup growth in RAAGs and RAAGs with Coxeter relations.
method Analyzing the independence number of defining graphs for RAAGs and conjecturing for RAAGs with Coxeter relations.
result Subgroup growth rate depends on the independence number of the defining graph for RAAGs and a conjecture for RAAGs with Coxeter relations.
The work of Jørgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. In this paper, we construct examples showing that the number of hyperbolic knot complements with a given volume v can grow at least factorially fast with v. A similar statement holds…
In this paper, we develop a parameter estimation method for factorially parametrized models such as Factorial Gaussian Mixture Model and Factorial Hidden Markov Model. Our contributions are two-fold. First, we show that the emission matrix of the standard Factorial Model is unidentifiable even if the true assignment ma…
Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial "sparse" methodology. We derive a large …
We study a novel spline-like basis, which we name the "falling factorial basis", bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations in basis matrix multiplication and basis matrix inversion. The falling factoria…
Special covers of alternating links have finite index subgroups in certain groups.
problem Understanding the structure of alternating link complements and their subgroups.
method Constructing special covers with bounded degree and embedding into specific groups.
result Explicit bounds on the index of subgroups in right-angled Artin and Coxeter groups.
New factorial power constants improve optimization convergence rates.
problem Optimization convergence rates depend on various constants.
method Proposes using factorial powers for defining these constants.
result Factorial powers simplify or improve convergence rates of optimization methods.
Bayesian neural networks improve uncertainty estimation in 3D point cloud segmentation for factory planning.
problem Improving uncertainty estimation in 3D point cloud segmentation for factory planning.
method Proposed fully Bayesian and approximate Bayesian neural networks for point cloud segmentation.
result Superior model performance and improved segmentation results with uncertainty incorporation.
Neural networks learn more efficiently with hidden factorial structures.
problem Challenges in high-dimensional statistical learning.
method Controlled experimental framework to test neural networks' ability to exploit hidden factorial structures.
result Neural networks can leverage hidden factorial structures to learn discrete distributions more efficiently.
Factorial moments are convenient tools in nuclear physics to characterize the multiplicity distributions when phase-space resolution (Δ) becomes small. For uncorrelated particle production within Δ, Gaussian statistics holds and factorial moments Fq are equal to unity for all orders q. Correlations between par…
This paper tackles efficient learning for factorial marked temporal point processes.
problem Efficient learning for factorial marked temporal point processes.
method Decoupled learning method with two procedures: ADM-M and Fast ISTA, and a reformulated Logistic Regression model.
result Empirical results show the efficiency of the decoupled and reformulated method.
Designs efficient factorial experiments for product design under budget constraints.
problem Designing effective experiments for product design with limited traffic and overlapping experiments.
method Two-stage design: first stage samples and infers performance, second stage selects a final policy.
result The method outperforms one-shot tensor completion and unstructured best-arm benchmarks.
New method uses Rashomon sets to improve Bayesian inference in factorial designs.
problem Combustion of model uncertainty in factorial designs leads to multimodal posterior and convergence issues.
method Rashomon-seeded annealing, integrating high-performing models as warm start for AIS.
result Restores full posterior inference without exhaustive enumeration of model space.
New algorithms for high-dimensional HMMs reduce complexity by discarding non-local factors.
problem High-dimensional HMMs are computationally expensive to filter and smooth.
method Approximate filtering and smoothing via locality in factor graphs, avoiding exponential cost.
result Error bounds in local total variation norm are dimension-free, improving scalability.
New findings show single-treatment effects are unidentifiable in factorial experiments.
problem Identifying the effect of a single intervention in factorial experiments.
method Formalized sufficient conditions for the identifiability of single-treatment effects and developed nonparametric sharp bounds.
result Researchers must justify assumptions for extrapolating single-treatment effects.
High-throughput 3D control training system achieves 100,000 FPS.
problem Lack of efficient, single-machine reinforcement learning systems.
method Sample Factory combines asynchronous sampling and off-policy correction.
result Achieves 100,000 FPS on 3D control problems without sacrificing sample efficiency.
Study sharp convergence rates of empirical UOT for spatio-temporal point processes.
problem Statistical analysis of UOT for spatio-temporal point processes.
method Empirical plug-in estimators for Kantorovich-Rubinstein distance between intensity measures.
result Sharp convergence rates of empirical UOT in terms of intrinsic dimensions of measures.
The past decade has seen substantial work on the use of non-negative matrix factorization and its probabilistic counterparts for audio source separation. Although able to capture audio spectral structure well, these models neglect the non-stationarity and temporal dynamics that are important properties of audio. The re…
Proposes a new prior for deep generative models to capture latent properties.
problem Complex non-linear relationships between data and latent properties.
method Factorial mixture prior with Gaussian mixture models for quantization.
result Empirically evaluated method for learning discrete properties in unsupervised or semi-supervised settings.
Factorial moments are convenient tools in particle physics to characterize the multiplicity distributions when phase-space resolution (Δ) becomes small. They include all correlations within the system of particles and represent integral characteristics of any correlation between these particles. In this letter, we sh…
Prediction Factory automates predictive model development and evaluation.
problem Rapidly developing and sharing predictive models with domain experts.
method Data science automation system with three interfaces: baseline, full, and optional automation.
result Full automation interface generated reports funded 57.5% of the time, compared to 42.5% for baseline.
Existence of Kähler-Einstein metrics on toric varieties proven.
problem Existence of Kähler-Einstein metrics on toric varieties.
method Characterization of K-stability using log Cox ring and universal orbifold cover.
result Every Q-factorial normal projective toric variety allows an orbifold Kähler-Einstein metric.
We prove the factoriality of the following nodal threefolds: a complete intersection of hypersurfaces F and G⊂P5 of degree n and k respectively, where G is smooth, ∣Sing(F∩G)∣⩽(n+k−2)(n−1)/5, n⩾k; a double cover of a smooth hypersurface $F\subset\mathbb{P}^{…
NoMoPy models noise as HMM/FHMM in Python.
problem Modeling noise in data.
method Approximate and exact EM algorithms, cross-validation, confidence region estimation.
result Validated on example problems.
A new method, FactorVAE, learns disentangled representations from independent factors.
problem Unsupervised learning of disentangled representations from independent factors.
method FactorVAE encourages factorial distribution of representations to be independent across dimensions.
result FactorVAE improves disentanglement over β-VAE by better balancing disentanglement and reconstruction quality. Factorial Hidden Markov Models (FHMMs) are powerful models for sequential data but they do not scale well with long sequences. We propose a scalable inference and learning algorithm for FHMMs that draws on ideas from the stochastic variational inference, neural network and copula literatures. Unlike existing approaches…
CUBE explains models by balanced experiments and contrasts.
problem Post-hoc explanation of trained predictive models.
method Design-based framework using balanced low-high probes.
result Reveals dominant learned effect structure and clarifies query efficiency.
Bayesian segmentation and uncertainty estimation improve 3D model accuracy for factory planning.
problem Generating accurate 3D models from outdated and incomplete 2D data.
method Bayesian neural network for point cloud segmentation and entropy-based uncertainty estimation.
result Bayesian segmentation network significantly improves model accuracy and object identification.
This work speeds up fHMM analysis by tensor algebra.
problem Scalability issues in analyzing factorial hidden Markov models.
method Tensorized algorithms and scalable filtering methods.
result Significant improvement in computational performance.
Bayesian inference for factorial hidden Markov models is challenging due to the exponentially sized latent variable space. Standard Monte Carlo samplers can have difficulties effectively exploring the posterior landscape and are often restricted to exploration around localised regions that depend on initialisation. We …
Bayesian CNN estimates uncertainty in bone age prediction.
problem Uncertainty quantification in age estimation models.
method Variational Inference for Bayesian CNNs.
result Model uncertainty distinguished from data uncertainty.
A new approach to sensitivity analysis without the Sobol decomposition.
problem Traditional sensitivity indices like Sobol indices have limitations.
method Introducing sensitivity measures that generalize existing indices and define interaction effects.
result Sensitivity measures can create new indices and define interaction effects.
New model estimates unknown number of users in asynchronous multiuser communication.
problem Estimating unknown number of users in asynchronous multiuser communication.
method Infinite factorial finite state machine model with Bayesian nonparametric approach.
result Effective recovery of data-generating process for various scenarios.
The paper describes a cover of strata of k-differentials with a formula for fiber cardinality.
problem Understanding the ramification locus and cardinality of fibers in strata of k-differentials.
method Intersection calculations on multi-scale compactification and flat geometry.
result A formula for the cardinality of each fiber involving the k-factorial function.
Study properties of algebraic threefolds with specific singularities.
problem Characterize and classify algebraic threefolds with certain singularities.
method Use topological invariants, rational homology, Poincaré duality, and Lie algebras.
result Relate topological invariants to Lie algebras and representations.
Study optimizes CANN for actuarial tasks using RSM.
problem Optimizing hyperparameters for neural networks in actuarial science.
method Factorial design and response surface methodology (RSM).
result Reduced hyperparameter optimization from 288 to 188, achieving near-optimal performance.
Factorial hidden Markov models (FHMMs) are powerful tools of modeling sequential data. Learning FHMMs yields a challenging simultaneous model selection issue, i.e., selecting the number of multiple Markov chains and the dimensionality of each chain. Our main contribution is to address this model selection issue by exte…
DABS uses a policy network to select experiments in high-dimensional design spaces.
problem Adaptive factorial screening in high-dimensional discrete design spaces.
method DABS learns a policy network offline to sequentially select experiments, incorporating sparsity and interactions via a spike-and-slab prior.
result DABS achieves superior accuracy and scalability over classical and Bayesian baselines under tight experimental budgets.
A new experimental design method for combinatorial interventions reduces complexity and improves accuracy.
problem Efficiently conducting all possible combinatorial interventions with multiple treatments and potential interactions.
method Probabilistic factorial experimental design, applying random combinations of treatments and adapting over multiple rounds.
result Optimal dosage of 1/2 for each treatment yields near-optimal design for estimating any k-way interaction model.
Proposes BSSP to stabilize predictions in biased data.
problem Distribution shift between training and test data causes prediction instability.
method Balance-subsampled stable prediction (BSSP) algorithm based on fractional factorial design.
result Significantly improves prediction stability across unknown test data.
New method disentangles sources of different timescales in planetary seismic data.
problem Unsupervised source separation of multi-scale seismic data from planetary missions.
method Wavelet scattering spectra for multi-scale clustering and variational autoencoder for source separation.
result Disentangles sources with different timescales in InSight mission seismic data.
Generative models improved with smoothed score functions for better sample quality.
problem Improving generative models for better sample quality.
method Smoothed score functions based on factorial Gaussian kernels.
result Single noise level achieved 14.15 Fréchet inception distance on CIFAR-10.
This expository article describes applications of topological configuration spaces to the control of robotic systems. In particular, we review recent work by the authors on configuration spaces of graphs. These are lovely spaces: we show for example that the configuration space of two points on the complete graph of fi…
We count the number of conjugacy classes of maximal, genus g, surface subroups in hyperbolic 3-manifold groups. For any closed hyperbolic 3-manifold, we show that there is an upper bound on this number which grows factorially with g. We also give a class of closed hyperbolic 3-manifolds for which there is a lower bound…
Deep model learns complex latent codes without assuming factor structure.
problem Learning latent codes with complex, non-factorial distributions.
method Deep generative factor analysis with beta process prior and stochastic EM algorithm.
result Preliminary results show model can approximate complex distributions.
Paper adapts causal analysis for time-dependent systems, especially energy management.
problem Challenges in root-cause analysis for systems with lagged time-dependencies, particularly in energy management.
method Adapts causal root-cause analysis method to time-dependent systems, discusses two truncation approaches.
result Extension effectively localizes root-causes in feature and time domain with enough lags.
Complex Chern-Simons theory reveals peacock patterns in perturbative series.
problem Understanding the structure of partition functions in complex Chern-Simons theory.
method Analyzing the partition function as a holomorphic function and using resurgence theory.
result Perturbative series are resurgent, with trans-series involving non-perturbative variables.