PolyILR: A Tree-Structured Orthonormal Decomposition of Compositional Data
problem Representing compositional data with hierarchical structure
method PolyILR: A canonical orthonormal decomposition of the Aitchison tangent space aligned with any tree topology
result PolyILR yields stable, interpretable features and enables inference at multiscale tree resolution
Develops methods for valid and validated confidence sets in multiclass and multilabel prediction.
problem Challenges of typical conformal prediction methods in multiclass and multilabel problems, especially uneven coverage.
method Leverages quantile regression to build methods that always guarantee correct coverage and asymptotically optimal conditional coverage, addressing label interactions with tree-structured classifiers.
result Empirical evaluation suggests more robust coverage of confidence sets.
The paper tackles the computational complexity of PLT algorithms, providing tractable solutions.
problem Finding a tree structure that results in a PLT with low computational costs and low statistical error.
method The paper shows that finding an optimal tree structure is NP-complete. It provides linear time solutions for specific cases and an O(logm) approximation for the general case. result The paper provides tractable solutions for finding a tree structure with low computational costs and low statistical error.
A hierarchical routing mixture of experts model for complex regression tasks.
problem Complex data distribution in regression tasks.
method Binary tree-structured hierarchical routing mixture of experts (HRME) model with classifiers and simple regression models.
result Effective prediction with simple leaf experts in multimodal data.
In this paper, we present a new approach to learning cascaded classifiers for use in computing environments that involve networks of heterogeneous and resource-constrained, low-power embedded compute and sensing nodes. We present a generalization of the classical linear detection cascade to the case of tree-structured …
Paper studies multiclass classifiers from binary classifiers, proving methods and demonstrating advantages.
problem Constructing efficient multiclass classifiers from binary ones.
method Two methods: one vs. all and hierarchical classification, with a new leverage-hierarchical method introduced.
result Proves upper bounds and exact formulas for multiclass regret in terms of binary regrets.
The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on the learning rate as the number of samples increases is discussed. Specifically, the error…
New tree structure for pseudo-Anosovs from interval maps.
problem Understanding pseudo-Anosovs from interval maps.
method Tree structure on pseudo-Anosovs using rational numbers.
result Deepened dictionary between invariants.
Study a risk model with tree-structured Poisson-Markov random field for rainfall events.
problem Dependence between rainfall frequencies in insurance portfolios.
method Tree-structured Markov random field with Poisson marginals.
result Asymptotic results for portfolio risk and risk allocation.
Adversarial edit attacks improve machine learning model security for tree data.
problem Improving security of machine learning models for tree-structured data.
method Extends adversarial attacks to tree-structured data using tree edit distance and black-box queries.
result Many tree classifiers can be effectively attacked, demonstrating the vulnerability of these models.
Probabilistic label trees improve XMLC by organizing labels hierarchically.
problem Efficiently tagging instances with a small subset of relevant labels from a large pool.
method Introduce and analyze probabilistic label trees (PLTs) as a generalization of hierarchical softmax for multi-label problems.
result PLTs are consistent for various performance metrics and can be trained online without prior knowledge.
End-to-end learning framework for tree-structured data.
problem Learning models struggle with tree-structured data due to lack of fixed-length vectors.
method Developed a novel framework for generic semantic tree-structured data of arbitrary topology.
result Framework yields comparable performance to standard models with dedicated feature-vectors and outperforms in compositional data.
Paper presents a new method for learning hyperbolic representations using tree structures.
problem Learning faithful low-dimensional hyperbolic embeddings of data.
method Metric-first approach to learn tree structure, then embed into hyperbolic manifold.
result Novel fast algorithm TreeRep learns tree approximating original metric.
TS-CHIEF improves TSC accuracy while drastically reducing runtime.
problem Infeasibility of HIVE-COTE for large datasets.
method Combines time series embeddings into a tree-structured classifier.
result Achieves state-of-the-art accuracy with 130k time series in 2 days.
Optimal rates for learning hidden tree structures are determined.
problem Learning hidden tree structures from noisy data.
method Study of the (noisy) information threshold and the Chow-Liu algorithm.
result Optimal rates for structure recovery are inversely proportional to the information threshold squared.
Paper tackles robust estimation of tree-structured Ising models without side information.
problem Learning tree-structured Ising models with flipped signs of variables.
method Proves unidentifiability, proposes an algorithm with logarithmic sample complexity and polynomial run-time complexity.
result Empirically demonstrates robustness of proposed algorithm in the flipped signs setting.
The paper uses tensor decompositions to improve neural network models for tree data.
problem Encoding structural knowledge from tree-structured data efficiently.
method Introduces new aggregation functions using Canonical and Tensor-Train decompositions.
result Proposed models outperform traditional methods on tree classification tasks.
New method solves tree-structured Schrödinger Bridge problems.
problem Computing Schrödinger Bridge between tree-structured distributions.
method Iterative Markovian Fitting (IMF) procedure for tree-structured costs.
result Extends IMF to tree-structured Schrödinger Bridge problems.
We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of particles (representing the objects) diffusing in some continuous space, analogou…
Extends neural network approximation to probability measures and tree-structured data.
problem Universal approximation of functions on probability measures and tree-structured domains.
method Proof of neural network density in probability measure spaces and Cartesian products.
result Universal approximation theorem for tree-structured domains, including JSON.
Exact learning of tree-structured models with side info and noise.
problem Learning tree-structured graphical models with side information and noise.
method Probabilistic tools from strong large deviations theory.
result Exact asymptotics of structure learning from samples.
Dealing with uncertainty in Bayesian Network structures using maximum a posteriori (MAP) estimation or Bayesian Model Averaging (BMA) is often intractable due to the superexponential number of possible directed, acyclic graphs. When the prior is decomposable, two classes of graphs where efficient learning can take plac…
Enhances projection pursuit tree classifier with visual diagnostics for better multi-class classification.
problem Rigidity of original algorithm limits performance in complex high-dimensional classification problems.
method Allowing more splits and flexible class groupings in projection pursuit computation, and developing visual diagnostics.
result Demonstrates enhanced classifier performs as intended through interactive visual diagnostics.
Improved Bayesian optimization for conditional parameter spaces.
problem Efficient global optimization of expensive-to-evaluate functions in conditional parameter spaces.
method Additive tree-structured covariance function for conditional parameter optimization.
result Significantly improved sample-efficiency and wider applicability compared to existing methods.
We propose a new splitting criterion for a meta-learning approach to multiclass classifier design that adaptively merges the classes into a tree-structured hierarchy of increasingly difficult binary classification problems. The classification tree is constructed from empirical estimates of the Henze-Penrose bounds on t…
New tree-structured Markov fields with Poisson marginals for counting variables.
problem Counting variables with complex dependencies.
method Tree-structured Markov random fields with Poisson marginals.
result Straightforward sampling and joint probability calculations.
Novel covariance function improves Bayesian optimization efficiency.
problem Efficient global optimization of expensive black-box functions.
method Additive tree-structured covariance function and parallel optimization algorithm.
result Significantly outperforms state-of-the-art methods in conditional parameter optimization.
In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree structure, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and a diameter bound f…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models, hidden Markov models, Gaussian mixture models, and Markov evolutionary trees. The …
Bayesian tensor factorization approximates a complex tree model.
problem Intractable size of state-transition matrix in Hidden Tree Markov Models.
method Tucker factorization of tensors for probabilistic interpretation.
result New model outperforms existing approximations on tree-structured data tasks.
The paper tackles high-dimensional Bayesian optimization using tree-structured additive models.
problem Scaling Bayesian Optimization to high-dimensional problems.
method Tree-structured additive models with hybrid graph learning and zooming-based algorithms.
result Demonstrates faster model learning and reduced model complexity in high-dimensional settings.
Additive models, such as produced by gradient boosting, and full interaction models, such as classification and regression trees (CART), are widely used algorithms that have been investigated largely in isolation. We show that these models exist along a spectrum, revealing never-before-known connections between these t…
Tree-Transformer improves grammar correction in code and natural language.
problem Grammar correction in tree-structured data.
method Tree-Transformer neural network architecture for tree-structured data.
result Significant improvement in grammar correction accuracy.
Innovative PGMs match neural networks, revealing precise approximations during forward propagation.
problem Lack of precise semantics and probabilistic interpretation in neural networks.
method Constructing infinite tree-structured PGMs that correspond to neural networks.
result DNNs perform precise approximations of PGM inference during forward propagation.
Improved algorithm for partial recovery of tree-structured graphs with noisy data.
problem Learning Ising tree models with noisy observations.
method Symmetrized Geometric Averaging (SGA) algorithm with improved sample complexity.
result Significantly better sample complexity for partial tree recovery.
In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central machine is then responsible for learning the structure based on received messag…
The problem of maximum-likelihood (ML) estimation of discrete tree-structured distributions is considered. Chow and Liu established that ML-estimation reduces to the construction of a maximum-weight spanning tree using the empirical mutual information quantities as the edge weights. Using the theory of large-deviations…
The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions based on Bayesian learning of clique tree decomposition is presented. The main contr…
Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attain low classification errors. The resulting classifier is linear in the log-transformed univariate and b…
Study recovers tree structure in noisy MRFs with support size 3 or more.
problem Learning tree-structured MRFs with symmetric noise.
method Characterized recoverability based on joint PMF, provided algorithm for recovery.
result Structure of leaf clusters can be partially or fully identifiable.
New clustering method recovers hidden tree structure from data.
problem Recovering hidden hierarchical structure in data.
method Maximum average dot product for merging clusters in hierarchical clustering.
result The algorithm produces a tree that accurately represents the underlying generative hierarchical structure.
USNRT uses tree-structured learning to improve uncertainty quantification of variance networks.
problem Improving uncertainty quantification of variance networks.
method Tree-structured local neural network model that partitions feature space into regions for training region-specific neural networks to predict mean and variance.
result USNRT shows superior performance in estimating uncertainty with variances on UCI datasets compared to recent methods.
We construct a partial order relation which acts on the set of 3-cliques of a maximal planar graph G and defines a unique hierarchy. We demonstrate that G is the union of a set of special subgraphs, named `bubbles', that are themselves maximal planar graphs. The graph G is retrieved by connecting these bubbles in a tre…
Tree-AMP simplifies inference in complex tree-structured models.
problem Inference in high-dimensional tree-structured models.
method Approximate Message Passing algorithms for various machine learning tasks.
result Theoretical performance predictions and automated entropy estimation.
Study shows linear sample complexity for learning SPNs.
problem Learning the set of distributions represented by Sum-Product Networks (SPNs).
method Initiate study of sample complexity, show linear growth up to logarithmic factors, use distribution compression schemes.
result Sample complexity grows linearly with the number of parameters of the SPN.
TreeDSB solves mOT problems on tree-structured costs for Wasserstein barycenters.
problem Optimal transport with multiple marginals and tree-structured quadratic costs.
method Tree-based Diffusion Schrödinger Bridge (TreeDSB) for continuous and dynamic solutions.
result TreeDSB efficiently computes Wasserstein barycenters in high dimensions.
Optimal transport for measures on noisy tree metrics is solved with robust approach.
problem Optimal transport problem for measures on noisy tree metrics.
method Max-min robust optimal transport approach considering uncertainty sets of tree metrics.
result Robust optimal transport admits a closed-form expression for fast computation.
We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove som…