We introduce in this paper a new way of optimizing the natural extension of the quantization error using in k-means clustering to dissimilarity data. The proposed method is based on hierarchical clustering analysis combined with multi-level heuristic refinement. The method is computationally efficient and achieves bett…
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48 results for “Hierarchical Refinement”
Generates infinite-depth hierarchical clusters from few examples.
problem Inadequate finite-sample clustering methods for fine-scale hierarchical structures.
method Classification fields generated by a local refinement rule, approximated by predictors.
result Learned predictors can approximate infinite-depth hierarchical structures.
Bayesian Hierarchical Invariant Prediction refines ICP for better scalability and prior integration.
problem Improving computational scalability and invariance testing for causal inference.
method Bayesian Hierarchical structure to test invariance under heterogeneous data.
result Demonstrated improved scalability and potential as an alternative to ICP.
Algorithm refines matrix ratings using hierarchical graph clustering.
problem Matrix completion with side information from social graphs.
method Hierarchical graph clustering followed by iterative refinement of matrix ratings.
result Achieves optimal sample complexity for matrix completion.
Automated Intracranial Artery Labeling using a Graph Neural Network and Hierarchical Refinementcs.CV
Automated labeling of intracranial arteries improves accuracy and efficiency.
problem Challenges in accurately labeling intracranial arteries due to variations and limited datasets.
method Graph Neural Network (GNN) combined with hierarchical refinement for improved accuracy.
result Achieved 97.5% node labeling accuracy on a testing set of 105 scans.
Improved portfolio optimization using machine learning and hierarchical clustering.
problem Suboptimal out-of-sample performance and unrealistic allocations in the Markowitz Model.
method Refined Markowitz Model with hierarchical clustering-based approach.
result Enhanced portfolio performance on a risk-adjusted basis.
Locally-verifiable conditions ensure exactness of spline discrete de Rham complex.
problem Ensuring cohomological equivalence of spline discrete complex to continuous de Rham complex.
method Theoretical analysis and locally-verifiable sufficient conditions for exactness.
result Locally-verifiable conditions guarantee exactness of hierarchical B-spline discrete de Rham complex.
Method learns hierarchical representations of samples and features simultaneously.
problem Hierarchical structures in samples and features not considered by existing methods.
method Jointly learns hierarchical representations via Tree-Wasserstein Distance alternating between samples and features.
result Method improves performance in link prediction and node classification tasks.
Improved hierarchical discrete VAEs for better stability and performance.
problem Training stable and efficient hierarchical discrete VAEs with numerous latent variables.
method Introducing Relaxed-Responsibility Vector-Quantisation to parameterise discrete latent variables in a hierarchical structure.
result Achieved state-of-the-art bits-per-dim results for various standard datasets.
Multi-Output Dependence (MOD) learning is a generalization of standard classification problems that allows for multiple outputs that are dependent on each other. A primary issue that arises in the context of MOD learning is that for any given input pattern there can be multiple correct output patterns. This changes the…
Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampli…
We prove a geometric model for HHS hierarchies as CAT(0) cube complexes.
problem Modeling hierarchically hyperbolic spaces as cube complexes.
method Prove quasi-median quasi-isometry between hulls and cubical models.
result Hierarchical boundaries are locally modeled by CAT(0) cube complexes.
MGDL refines deep neural networks by training grades sequentially, improving stability.
problem Training deep neural networks is challenging due to nonconvex optimization landscapes.
method MGDL trains deep networks grade by grade, freezing previously learned grades and training new ones to fit residuals.
result MGDL guarantees vanishing error in a fixed-width multigrade ReLU architecture.
THEME: Enhancing Thematic Investing with Semantic Stock Representations and Temporal Dynamicsq-fin.PM
Enhances thematic investing with stock embeddings from textual data.
problem Challenges in constructing thematic portfolios due to overlapping sector boundaries and evolving market dynamics.
method Introduces THEME, a framework that fine-tunes embeddings using hierarchical contrastive learning, aligning themes and stocks using their hierarchical relationship and incorporating stock returns.
result Theme-aligned portfolios demonstrate compelling performance, significantly outperforming large language models in thematic asset retrieval.
CCVFM uses coreset to improve generative models by refining residual flows.
problem Generating multimodal distributions from scratch is challenging.
method Augments hierarchical rectified flow with a data-informed source distribution using a coreset.
result CCVFM achieves competitive few-step generation without a learned noise-to-data map.
Tab-TRM uses recursive model for insurance pricing on tabular data.
problem Insurance pricing on tabular data.
method Adapts recursive latent reasoning to insurance modeling using a compact, parameter-efficient network.
result Improves insurance pricing accuracy using iterative refinement of latent tokens.
Graph convolutional networks (GCNs) have been successfully applied in node classification tasks of network mining. However, most of these models based on neighborhood aggregation are usually shallow and lack the "graph pooling" mechanism, which prevents the model from obtaining adequate global information. In order to …
Nested learning improves model performance on multi-granular tasks.
problem Overconfident models and lack of fine-grained confidence in predictions.
method Introducing nested learning with a sequence of nested feature embeddings and explicit combination of outputs.
result Nested learning outperforms standard end-to-end training on various datasets.
Unified framework for DRO and DTA using Bayesian nonparametrics.
problem Combining DRO and DTA under ambiguity.
method Unified framework using DP and HDPs, with outlier robustness.
result Favorable performance in prediction accuracy and stability.
Enhances POU-Nets with probabilistic noise model for efficient spatial data clustering.
problem Improving the efficiency and accuracy of deep learning models for spatial data.
method Integrates Gaussian noise model into POU-Nets to enable gradient-based optimization and hierarchical refinement.
result Achieves sharp spatial partitions and higher-order polynomial approximation without regularizers.
Adapts category theory to manifold learning for better understanding and stability.
problem Understanding and improving manifold learning algorithms.
method Develops a functorial perspective on manifold learning, proving bounds and constructing new algorithms.
result Derives new manifold learning algorithms that are competitive with existing methods.
V-HMN integrates memory mechanisms for improved image recognition.
problem Limited interpretability and high data requirements of existing vision backbones.
method Brain-inspired hierarchical memory modules with iterative refinement.
result V-HMN achieves strong performance on image classification benchmarks.
We present a reinforcement learning approach for detecting objects within an image. Our approach performs a step-wise deformation of a bounding box with the goal of tightly framing the object. It uses a hierarchical tree-like representation of predefined region candidates, which the agent can zoom in on. This reduces t…
Improved RL training for DMs reduces mode collapse and preserves diversity.
problem Mode collapse and training instability in RL fine-tuned diffusion models.
method Dynamic hierarchical RL training with sliding-window parameter regularisation.
result Models trained with HRF achieve better preservation of diversity in downstream tasks.
This paper tackles fitting multilevel low rank matrices by addressing three problems.
problem Fitting a given matrix by an MLR matrix in the Frobenius norm.
method Factor fitting, rank allocation, and hierarchical partitioning.
result The proposed methods can fit a given matrix by an MLR matrix in the Frobenius norm.
AJL framework detects dynamic patterns in high-dimensional time-varying models.
problem Complex time-varying associations and abrupt regime shifts in longitudinal processes.
method Hierarchical regularization framework integrating functional variable selection with structural changepoint detection.
result The refined estimator achieves the oracle property in ultra-high-dimensional settings.
Refining Coarse-grained Spatial Data using Auxiliary Spatial Data Sets with Various Granularitiesstat.ML
We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data set…
We study the problem of building generative models of natural source code (NSC); that is, source code written and understood by humans. Our primary contribution is to describe a family of generative models for NSC that have three key properties: First, they incorporate both sequential and hierarchical structure. Second…
The recent state-of-the-art deep learning methods have significantly improved brain tumor segmentation. However, fully supervised training requires a large amount of manually labeled masks, which is highly time-consuming and needs domain expertise. Weakly supervised learning with scribbles provides a good trade-off bet…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient methods are needed. We propose a new method that is based on a decomposition of the…
AdaPID optimizes diffusion-based samplers by dynamically adjusting schedules.
problem Optimizing the intermediate-time dynamics in diffusion-based samplers.
method Develops a time-varying stiffness schedule using Piece-Wise-Constant (PWC) parametrizations and a hierarchical refinement approach.
result QoS-driven PWC schedules consistently improve sampling fidelity and accuracy.
A scalable Bayesian inference method for mixed-effects models in systems biology.
problem Scalable Bayesian inference for complex hierarchical mixed-effects models in systems biology.
method Constructing amortized approximations of likelihood and posterior distributions, refined for each individual dataset.
result Our method is both fast and competitive in statistical accuracy compared to exact pseudomarginal Bayesian inference.
New inequality for refined knot invariants in a specific space.
problem General adjunction inequality for refined -invariants does not hold.
method Introduced an adjunction inequality for a specific spatial refinement in .
result An adjunction inequality holds for the -version of the -refinement in .
Paper introduces hierarchical softmax for global hierarchical classification tasks.
problem Improving classification accuracy in tasks with class hierarchies.
method Global hierarchical neural networks using hierarchical softmax.
result Hierarchical softmax outperforms regular softmax in multiple datasets.
We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which co…
This research improves multitask learning by creating task-specific pathways.
problem Creating task-specific representations for efficient learning.
method Developed generalization bounds for learning multiple tasks over multiple pathways.
result Proves the superiority of multipath representation over traditional shallow supernets.
Variational Auto-Encoders (VAEs) have been widely applied for learning compact, low-dimensional latent representations of high-dimensional data. When the correlation structure among data points is available, previous work proposed Correlated Variational Auto-Encoders (CVAEs), which employ a structured mixture model as …
GBOC detects anomalies in time series data using granular-ball vectors.
problem Challenges in modeling normal behavior in dynamic, nonlinear time series data.
method Granular-ball Vector Data Description (GVDD) and Granular-ball One-Class Network (GBOC).
result GBOC improves anomaly detection in time series data.
Refines neural network predictions using background knowledge for improved accuracy.
problem Compensate for lack of labeled data in neural networks.
method Introduces differentiable refinement functions and Iterative Local Refinement (ILR) algorithm to refine predictions efficiently and accurately.
result ILR finds competitive results in MNIST addition task and refines predictions on complex SAT formulas.
New research shows label refinement and weak training have limitations for aligning LLMs.
problem Limitations of refinement methods for aligning large language models.
method Analyzed probabilistic assumptions and alternative approaches to label refinement and weak training.
result Label refinement and weak training suffer from irreducible error, leaving a performance gap.
This study compares hierarchical and non-hierarchical models for open-domain multi-turn dialog generation.
problem Which kind of models (hierarchical or non-hierarchical) is better for open-domain multi-turn dialog generation?
method Systematically compared nearly all representative hierarchical and non-hierarchical models over the same experimental settings.
result Nearly all hierarchical models are worse than non-hierarchical models in open-domain multi-turn dialog generation, except for HRAN.
HFNO enhances interpretability of turbulent flows through parallel wavenumber bin processing.
problem Opaque inner workings of Fourier Neural Operators (FNOs) hinder physical interpretability.
method Introduces HFNO, a novel FNO-based architecture that processes wavenumber bins in parallel, enhancing interpretability.
result HFNO decomposes turbulent flows across various scales, enabling increased interpretability and multiscale modeling.
We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we descr…
We refine Khovanov homology in the presence of an involution on the link. This refinement takes the form of a triply-graded theory, arising from a pair of filtrations. We focus primarily on strongly invertible knots and show, for instance, that this refinement is able to detect mutation.
Paper proposes a Renyi entropy-based method for tuning hierarchical topic models.
problem Tuning hierarchical topic models, especially determining the number of topics at each level, is challenging.
method The paper introduces a Renyi entropy-based metric for quality assessment and a practical tuning concept.
result The proposed method can estimate the number of topics for two hierarchical levels in hARTM model.
In a previous paper we constructed a spectrum-level refinement of Khovanov homology. This refinement induces stable cohomology operations on Khovanov homology. In this paper we show that these cohomology operations commute with cobordism maps on Khovanov homology. As a consequence we obtain a refinement of Rasmussen's …
Neural NMF discovers hierarchical topics in multilayer data.
problem Detecting latent hierarchical structure in multilayer data.
method Recursive application of nonnegative matrix factorization (NMF) in layers with backpropagation optimization.
result Neural NMF outperforms other hierarchical NMF methods in synthetic and real-world datasets.
Refined 3D indexhep-th
Refined 3D index uses surgery and gradings to distinguish 3-manifolds.
problem Distinguishing 3-manifolds and gauge theories phases.
method Dehn surgery presentation, ideal triangulation, and enhanced flavor symmetries.
result Invariance of refined index under various transformations.