New method recovers graph latent positions under edge differential privacy.
problem Recovering latent graph information from privatized graphs.
method Applying geometric insights to adjust statistical inference for privatized graphs.
result Achieves consistent recovery of latent positions under local edge differential privacy constraints.
Researchers prove inner product recovery is impossible in latent space models.
problem Recovering inner products in latent space models with random geometric graphs.
method Rate-distortion theory applied to Gaussian or spherical latent locations.
result Impossible to recover inner products if dimensionality exceeds nh(p), matching positive results' conditions. New model captures state-dependent variability in partially observed systems.
problem Structured stochasticity not captured by constant-variance models.
method State-coupled stochastic volatility framework with particle expectation-maximization.
result Model consistently reduces recovery bias under partial observation.
We propose a neural network for unsupervised anomaly detection with a novel robust subspace recovery layer (RSR layer). This layer seeks to extract the underlying subspace from a latent representation of the given data and removes outliers that lie away from this subspace. It is used within an autoencoder. The encoder …
Paper models graph edge dependencies using latent variables for community detection.
problem Graphs' edge dependencies not fully explained by community membership.
method Introduces auxiliary latent variables to model edge dependencies and analyzes conditions for exact recovery.
result Exact recovery possible by semidefinite programming down to maximum likelihood threshold.
It is a well known fact that recovery rates tend to go down when the number of defaults goes up in economic downturns. We demonstrate how the loss given default model with the default and recovery dependent via the latent systematic risk factor can be estimated using Bayesian inference methodology and Markov chain Mont…
Study sharpens threshold for matching correlated graphs without labels.
problem Matching latent vertex correspondences in correlated random graphs.
method Analyzes information-theoretic limits for correct vertex matching in sub-sampled graphs.
result Establishes a sharp information-theoretic threshold for vertex matching recovery.
StrTransformer recovers sources without labels by optimizing latent matrices and enforcing structural constraints.
problem Unsupervised blind source recovery in signal processing.
method Source-wise structured Transformer framework with latent source matrix optimization, structural regularization, and branch-specific weights.
result StrTransformer learns distinct temporal-scale structures and recovers source-aligned latent trajectories.
A method estimates causal parameters using a latent variable recovery.
problem Estimating causal parameters in contexts with multiple causes and unobserved confounding.
method Substitute adjustment via recovery of latent variables.
result Substitute adjustment estimates adjusted regression parameters under certain conditions.
New method AnInfoNCE uncovers latent factors in contrastive learning with practical variability.
problem Theoretical assumptions of contrastive learning loss overlook practical variability in positive pairs.
method AnInfoNCE, a generalization of InfoNCE, models anisotropic variability to uncover latent factors.
result AnInfoNCE increases recovery of latent factors in CIFAR10 and ImageNet, albeit at the cost of accuracy.
This paper sets thresholds for recovering vertex correspondences in partially correlated graphs.
problem Recovering hidden vertex correspondences in partially correlated graphs.
method Proposed partially correlated Erdős-Rényi graphs model; information-theoretic thresholds; correlated functional digraphs.
result Optimal rates for partial and exact recovery of vertex correspondences.
Active seriation recovers item order from noisy pairwise similarity measurements.
problem Recovering an unknown item ordering from noisy pairwise similarity measurements.
method Proposes an active seriation algorithm that provably recovers the latent ordering with high probability.
result Establishes optimal performance guarantees for successful recovery under a uniform separation condition.
Improved graph embedding through refined linear transformation and community recovery.
problem Identifying meaningful latent communities in graph data.
method Refined graph encoder embedding via linear transformation, self-training, and latent community recovery.
result Improved vertex embedding and better decision boundaries for vertex classification.
Paper recovers latent causal structure and linear transformation from indirect observations.
problem Recovering latent causal structure and linear transformation from indirect observations.
method Established sufficient conditions for DAG recovery, leveraged score function properties, and used soft/hard interventions.
result Perfect recovery of latent DAG structure and linear transformation up to scaling using soft interventions, hard interventions with additional hypothesis testing.
Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a generative model. We search and constrain on latent variable space to make the m…
Study spectral properties of sparse random graphs to recover latent vectors.
problem Recovering latent vectors in sparse random geometric graphs.
method Analyzes spectral concentration and uses orthogonal polynomial expansions, decoupling, and matrix concentration.
result Sharpens spectral norm bounds and proves exact recovery for Gaussian mixture models.
Efficient algorithms for sparse parameter recovery in mixture models.
problem Support recovery of high-dimensional sparse latent vectors in mixture models.
method Efficient algorithms with logarithmic sample complexity dependence on dimensionality.
result First guarantees on support recovery for various mixture models.
There is empirical evidence that recovery rates tend to go down just when the number of defaults goes up in economic downturns. This has to be taken into account in estimation of the capital against credit risk required by Basel II to cover losses during the adverse economic downturns; the so-called "downturn LGD" requ…
GAME improves matrix completion by considering subgroup-specific latent structures.
problem Heterogeneous data with overlapping categories, smoothing away subgroup-specific variation.
method Group-Aware Matrix Estimation (GAME) with overlapping nuclear-norm penalties.
result GAME outperforms global low-rank estimators in structured missingness regimes.
New method solves linear inverse problems using diffusion models.
problem Linear inverse problems in various domains.
method Posterior sampling with latent diffusion models.
result Provable sample recovery in linear models, outperforming previous methods.
Exact recovery of tensor decomposition (TD) methods is a desirable property in both unsupervised learning and scientific data analysis. The numerical defects of TD methods, however, limit their practical applications on real-world data. As an alternative, convex tensor decomposition (CTD) was proposed to alleviate thes…
New model for multiplex networks learns shared structure.
problem Complex network structures not well modeled by existing methods.
method Latent space model for multiplex networks with shared structure.
result Model recovers latent positions with sufficient separation.
A new model explains U- and Swoosh-shaped stock price recovery during the COVID-19.
problem Modeling stock price recovery during the COVID-19 with V- and L-shaped recovery.
method Introducing a sentiment variable θ to quantify investor sentiment and simulate U- and Swoosh-shaped recovery. result The model explains U- and Swoosh-shaped recovery of sectoral indices with positive sentiment.
New spectral clustering method handles discrete covariates for better community detection.
problem Community detection in networks with discrete covariates.
method Spectral algorithm that separates latent network structure from observed covariates.
result Achieves perfect clustering with high probability in large, sparse networks.
Researchers improve tree model recovery from noisy data.
problem Learning tree structured models from corrupted data.
method Linear latent tree models and continuous corruption model.
result Chow-Liu algorithm consistently learns tree from noisy data.
A hierarchical model shows how scaling laws emerge from sequential feature recovery.
problem Emergence of scaling laws from feature learning in multi-layer networks.
method Layer-wise spectral algorithm adapted to compositional structure, sequential feature detection.
result Sequential detection of latent features, leading to explicit power-law decay of prediction error.
The Generator of a Generative Adversarial Network (GAN) is trained to transform latent vectors drawn from a prior distribution into realistic looking photos. These latent vectors have been shown to encode information about the content of their corresponding images. Projecting input images onto the latent space of a GAN…
Telecommunication (Telco) outdoor position recovery aims to localize outdoor mobile devices by leveraging measurement report (MR) data. Unfortunately, Telco position recovery requires sufficient amount of MR samples across different areas and suffers from high data collection cost. For an area with scarce MR samples, i…
Paper learns latent and hierarchical structures in CDMs from data.
problem Jointly learning latent and hierarchical structures in CDMs from observed data.
method Penalized likelihood approach for selecting attributes and estimating structures; EM and latent structure recovery algorithms.
result Good performance demonstrated by simulation and real data applications.
HCL learns shared and modality-specific latent representations for multimodal data.
problem Binary shared-private decomposition inadequately represents shared information across subsets of modalities.
method Hierarchical Contrastive Learning framework combining latent-variable formulation, structural sparsity, and contrastive objective.
result HCL accurately recovers hierarchical structure and improves predictive performance on multimodal data.
A new model integrates covariates with grade of membership analysis for better latent structure recovery.
problem Improving latent structure recovery in multivariate categorical data analysis.
method Covariate-assisted grade of membership model exploiting shared low-rank simplex geometry.
result Auxiliary covariates can provably improve latent structure recovery, leading to faster convergence rates.
Paper establishes identifiability and achievability for causal representation learning.
problem Identifying and recovering latent causal models and variables from observational and interventional data.
method Establishes identifiability and achievability using uncoupled interventions and a recovery algorithm.
result Guaranteed perfect recovery of latent causal model and variables under uncoupled interventions.
In sensing applications, sensors cannot always measure the latent quantity of interest at the required resolution, sometimes they can only acquire a blurred version of it due the sensor's transfer function. To recover latent signals when only noisy mixed measurements of the signal are available, we propose the Gaussian…
Framework for inferring latent structure from sparse, imperfectly detected bipartite networks.
problem Recovering latent structure from sparse, imperfectly detected bipartite networks in ecology.
method Structured sparse nonnegative low-rank factorization with detection probability estimation and ADMM-based algorithm.
result Improved recovery of latent factors and structure compared to existing methods.
Develops a new method to recover large latent tree models efficiently.
problem Inference of large latent tree structures from terminal node observations.
method Spectral Top-Down Recovery (STDR) using Fiedler vector partitioning.
result Proves statistical consistency and sample complexity for accurate tree recovery.
We find that factors explaining bank loan recovery rates vary depending on the state of the economic cycle. Our modeling approach incorporates a two-state Markov switching mechanism as a proxy for the latent credit cycle, helping to explain differences in observed recovery rates over time. We are able to demonstrate ho…
Paper proposes a fast algorithm to recover causal DAGs with latent variables.
problem Discovering causal relationships in the presence of latent variables.
method Cholesky factorization of covariance matrix with optimization for latent variables.
result The algorithm significantly outperforms previous methods in synthetic and real-world datasets.
Proposes using equivariant generative models for compressed sensing with unknown orientations.
problem Recovering signals with unknown orientations from underdetermined systems of linear measurements.
method Equivariant variational autoencoder as a generative prior for compressed sensing.
result Signals with unknown orientations can be recovered using iterative gradient descent on the latent space of equivariant models.
Latent DiTs improve data distribution recovery and inference efficiency under low-dimensional latent space.
problem Improving data distribution recovery and inference efficiency in latent DiTs.
method Investigates statistical and computational limits of latent DiTs under low-dimensional latent space assumption, deriving approximation error bounds, sample complexity, and efficient inference and training algorithms.
result Latent DiTs can bypass high dimensionality challenges and achieve almost-linear time inference and training.
A new method clusters intersecting lines using hypergraphs.
problem Clustering intersecting lines in subspace clustering.
method Constructing a geometric hypergraph and using spectral algorithm.
result Achieves information-theoretic bounds for line clustering.
The paper predicts responses on out-of-sample nodes using latent positions on unknown curves.
problem Predicting responses on out-of-sample nodes with latent positions on unknown curves.
method Manifold learning and graph embedding technique using latent positions.
result Convergence guarantees for predicting responses on out-of-sample nodes.
Generative adversarial networks (GANs) transform latent vectors into visually plausible images. It is generally thought that the original GAN formulation gives no out-of-the-box method to reverse the mapping, projecting images back into latent space. We introduce a simple, gradient-based technique called stochastic cli…
Proposes a method to recover sparse tensors with covariate info.
problem Sparse tensor with high missing entries and many zeros.
method Covariate-assisted Sparse Tensor Completion (COSTCO) using latent components.
result 23% accuracy improvement over baseline in advertisement dataset.
Identifiability, or recovery of the true latent representations from which the observed data originates, is de facto a fundamental goal of representation learning. Yet, most deep generative models do not address the question of identifiability, and thus fail to deliver on the promise of the recovery of the true latent …
Multi-view subspace clustering has been applied to applications such as image processing and video surveillance, and has attracted increasing attention. Most existing methods learn view-specific self-representation matrices, and construct a combined affinity matrix from multiple views. The affinity construction process…
Detection of dense cycles in graphs reveals a gap between easy detection and hard recovery.
problem Detecting and recovering dense cycles in Erdős-Rényi graphs.
method Characterization of computational thresholds for detection and recovery using low-degree polynomial algorithms.
result A gap exists between the detection and recovery thresholds for certain parameter regimes.
The question of how to determine the number of independent latent factors (topics) in mixture models such as Latent Dirichlet Allocation (LDA) is of great practical importance. In most applications, the exact number of topics is unknown, and depends on the application and the size of the data set. Bayesian nonparametri…
Compressed sensing techniques enable efficient acquisition and recovery of sparse, high-dimensional data signals via low-dimensional projections. In this work, we propose Uncertainty Autoencoders, a learning framework for unsupervised representation learning inspired by compressed sensing. We treat the low-dimensional …