SLIM model predicts social network polarization using signed links.
problem Polarization and filter bubbles in social networks.
method Signed relational Latent dIstance Model (SLIM) using Skellam distribution.
result SLIM model accurately predicts friendships and animosity in social networks.
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of space-forms. We next generalize results concerning metric rigidity via equations…
Characterizes higher rank model geometries using antipodal sets.
problem Identifying higher rank model geometries among Hadamard spaces.
method Using antipodal sets at infinity to characterize model geometries.
result Characterizes Riemannian symmetric spaces, Euclidean buildings, and products as higher rank model geometries.
New graph types help identify complex relationships.
problem Understanding complex relationships in data.
method Introducing separable and essentially separable graphs to characterize and identify graphical models.
result Developed algorithms to identify equivalence classes of essentially separable graphs.
We formulate and prove an axiomatic characterization of conditional information geometry, for both the normalized and the nonnormalized cases. This characterization extends the axiomatic derivation of the Fisher geometry by Cencov and Campbell to the cone of positive conditional models, and as a special case to the man…
New conditional risk measures called conditional generalized quantiles defined and characterized.
problem Developing new risk measures for dynamic risk assessment.
method Propose and characterize conditional generalized quantiles using expected utility model and equivalent conditions.
result Characterized conditional generalized quantiles as well-defined and equivalent to a conditional first order condition.
Paper characterizes optimal learning trajectories for high-dimensional nonlinear models.
problem Characterizing optimal learning trajectories in high-dimensional nonlinear models.
method Exploits maximum principle and dynamic programming for an optimal control problem of a gradient system.
result Constructs optimal learning trajectories leading to optimal model parameters.
Study characterizes cryospheric spectral feature space using joint PC+t-SNE approach.
problem Characterize cryospheric spectral feature space for remote sensing applications.
method Compare and contrast two approaches for identifying feature space basis vectors via dimensionality reduction (PCA and t-SNE).
result Joint characterization reveals distinct continua and clusters of ice reflectance properties.
This work improves density estimation by characterizing pdf complexity using NL-spectrum.
problem Improving density estimation rates for general probability densities.
method Introducing NL-spectrum to characterize pdf complexity and deriving dimension-independent rates of convergence.
result Dimension-independent rates of convergence for fast density estimation.
This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and by sharply characterizing the stationary covariance matrix of this process. The…
A hybrid method clusters and characterizes cancer data efficiently.
problem Challenges in clustering high-dimensional biomedical data.
method Gaussian mixture with generalized factor analyzers for efficient estimation.
result Our approach outperforms existing methods with faster convergence and higher accuracy.
New insights into X-ray transform on hyperbolic disk, with functional relations and range characterizations.
problem Understanding the X-ray transform on hyperbolic geometry.
method Derived new singular value decompositions, range characterizations, and intertwining relations with wedge-type differential operators.
result Sharp understanding of boundary behavior and invertibility settings for the X-ray transform.
Efficient synthetic data generation improves model performance on tabular data.
problem Improving model robustness and performance with scarce or low-quality data.
method Hardness characterization to identify high-value training points, generating synthetic data only from these points.
result Synthetic data generated from hardest points outperforms non-targeted methods on tabular datasets.
This paper addresses the log-optimal portfolio for a general semimartingale model. The most advanced literature on the topic elaborates existence and characterization of this portfolio under no-free-lunch-with-vanishing-risk assumption (NFLVR). There are many financial models violating NFLVR, while admitting the log-op…
Paper characterizes MDM for consumer choice modeling and prediction.
problem Modeling consumer choice behavior with parsimonious models.
method Establishes necessary and sufficient conditions for MDM consistency.
result Characterization leads to exact set of representable choice probabilities.
This paper characterizes VAE training pathologies and their effects on tasks.
problem Characterizing VAE training pathologies and their impact on downstream tasks.
method Concretely characterizing conditions for VAE training pathologies and their connection to specific downstream tasks.
result Connects VAE training pathologies to specific downstream tasks like learning compressed and disentangled representations, adversarial robustness, and semi-supervised learning.
Improves forecasting accuracy and uncertainty characterization for spatio-temporal data.
problem Lack of uncertainty characterization in classical and deep learning models for spatio-temporal data.
method Bayesian inference using particle flow for approximating the posterior distribution of hidden states.
result Our approach provides better uncertainty characterization while maintaining comparable accuracy.
Bi-Mamba model predicts diffusion coefficients and exponents from short data.
problem Characterizing anomalous diffusion in complex systems.
method Bidirectional state-space deep learning architecture.
result Efficient inference of diffusion coefficient and exponent from short trajectories.
Training deep learning models on mobile devices recently becomes possible, because of increasing computation power on mobile hardware and the advantages of enabling high user experiences. Most of the existing work on machine learning at mobile devices is focused on the inference of deep learning models (particularly co…
High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and rotated sparse vectors, etc. In this paper, we consider general superposition models …
We characterize the set of market models when there are a finite number of traded Vanilla and Barrier options with maturity T written on the asset S. From a probabilistic perspective, our result describes the set of joint distributions for (ST,supu≤TSu) when a finite number of marginal law constraint…
This paper proposes a new method to quantify uncertainty in reservoir characterization using invertible neural networks.
problem Quantifying uncertainty in reservoir characterization models.
method Training an invertible neural network to represent the posterior distribution of model parameters.
result The proposed method provides a more efficient and direct way to sample from the posterior distribution.
This paper characterizes how randomized neural networks generalize well in multi-dimensional tasks.
problem Understanding the generalization of randomized neural networks in multi-dimensional tasks.
method Characterizes RSNs as an IGAM formalized by an optimization problem with a regularization functional and loss.
result RSNs generalize well in multi-dimensional tasks, akin to spline regression under certain conditions.
Combines deep generative models with ensemble methods for subsurface property estimation.
problem Estimating spatially distributed subsurface properties from sparse measurements.
method Wasserstein Generative Adversarial Network (WGAN-GP) and Ensemble Smoother with Multiple Data Assimilation (ES-MDA).
result The proposed method outperforms variational inversion methods, especially for channelized and fractured fields.
We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an …
This paper characterizes projective models in statistical relational learning.
problem Projectivity in statistical relational models is beneficial for inference and learning.
method Representation theorems for infinite exchangeable arrays to characterize projective models.
result A class of directed graphical latent variable models correspond to projective relational models.
We extend Howie's characterization of alternating knots to give a topological characterization of toroidally alternating knots, which were defined by Adams. We provide necessary and sufficient conditions for a knot to be toroidally alternating. We also give a topological characterization of almost-alternating knots whi…
Geometric structures modeled on rational homogeneous manifolds are studied to characterize rational homogeneous manifolds and to prove their deformation rigidity. To generalize these characterizations and deformation rigidity results to quasihomogeneous varieties, we first study horospherical varieties and geometric st…
Study characterizes Einstein metrics in warped product spaces.
problem Characterizing Einstein metrics in warped product spaces.
method Local characterizations and global restatements of known results.
result Restated global characterizations of Einstein manifolds.
As Deep Learning (DL) models have been increasingly used in latency-sensitive applications, there has been a growing interest in improving their response time. An important venue for such improvement is to profile the execution of these models and characterize their performance to identify possible optimization opportu…
In this paper we introduce a simple model for a financial market characterized by a single stock or good and an interplay between two different traders populations, chartists and fundamentalists, which determine the price dynamic of the stock. The model has been inspired by the microscopic Lux-Marchesi model (T.Lux, M.…
We characterize distributional equivalence in latent-variable models with cycles.
problem Lack of an equivalence characterization for latent-variable causal models with cycles.
method Established graphical criterion for distributional equivalence and developed edge rank constraints.
result First equivalence characterization without structural assumptions for latent-variable models with cycles.
Understanding and characterizing the subspaces of adversarial examples aid in studying the robustness of deep neural networks (DNNs) to adversarial perturbations. Very recently, Ma et al. (ICLR 2018) proposed to use local intrinsic dimensionality (LID) in layer-wise hidden representations of DNNs to study adversarial s…
The study provides homological characterizations for Q-manifolds and l2-manifolds.
problem Density of maps in characterizing Q-manifolds and l2-manifolds. method Investigates weakening the density of Zn-maps and Z-maps to homological maps. result Obtains homological characterizations for Q-manifolds and l2-manifolds. The paper characterizes Alexander quandles of finite groups.
problem Characterizing Alexander quandles of finite groups.
method Using group theory and automorphism groups, the paper provides characterizations of Alexander quandles.
result Generalized Alexander quandles of finite groups are characterized in terms of automorphism groups and underlying groups.
We point out a new view on slow invariant manifolds (SIM) in dynamical systems which departs from a purely geometric covariant characterization implying coordinate independency. The fundamental idea is to treat the SIM as a well-defined geometric object in phase space and elucidate characterizing geometric properties t…
Generalizing Howie and Greene's characterization of alternating knots, we give a topological characterization of almost alternating knots.
No single parameter characterizes the learnability of probability distributions.
problem Finding a parameter to characterize the learnability of probability distributions.
method Analyzing various notions of learnability and showing impossibility results.
result No such parameter exists for characterizing learnability of probability distributions.
Characterizes super-replication prices in a financial market model.
problem Characterizing prices in a financial market model.
method Characterizes prices as the supremum of mono-prior super-replication prices through extreme priors and martingale measures.
result Super-replication prices are the supremum of mono-prior super-replication prices.
Characterizes deep neural network weight space for adversarial attacks.
problem Poor performance of deep learning models in adversarial examples.
method Characterizes deep neural network solution space using two paradigms.
result Adversarial attacks are less successful against Associative Memory Models.
Characterizes no Butterfly arbitrage in SVI model parameters.
problem No Butterfly arbitrage in SVI implied total variance formula.
method Characterization using intermediary condition from Fukasawa (2012) and rescaling of SVI parameters.
result Simple range conditions on SVI parameters ensure no Butterfly arbitrage.
Machine Learning (ML) is making a strong resurgence in tune with the massive generation of unstructured data which in turn requires massive computational resources. Due to the inherently compute- and power-intensive structure of Neural Networks (NNs), hardware accelerators emerge as a promising solution. However, with …
The application of deep learning techniques resulted in remarkable improvement of machine learning models. In this paper provides detailed characterizations of deep learning models used in many Facebook social network services. We present computational characteristics of our models, describe high performance optimizati…
Paper characterizes optimal language model alignment methods.
problem Aligning language models to maximize reward while keeping them close to the original model.
method KL-constrained reinforcement learning and best-of-N methods.
result Optimal KL-constrained RL solution has a large deviation principle rate function.
Characterizes the OU matrix for up to 5 strands in braids.
problem Understanding the structure of braid diagrams through their matrices.
method Characterization of the OU matrix for up to 5 strands in braids.
result Standard form of the OU matrix for general braids of up to 5 strands is given and characterized.
Generative models characterized through learning theory.
problem Characterizing generative models using learning theory.
method Formalized Gold, Angluin, and Kleinberg's results; introduced uniform and non-uniform generation; characterized closure dimension.
result Incompatibility between generatability and predictability for certain hypothesis classes.
Study provides concrete examples of knot slopes.
problem Finding explicit characterizing slopes for knots.
method Concrete examples for the (-2,3,7)-pretzel knot.
result Explicit characterizing slopes for the knot 12n242. Characterizes the sample complexity of list regression tasks.
problem Understanding the sample complexity of list learning tasks in regression.
method Introducing two combinatorial dimensions: k-OIG dimension and k-fat-shattering dimension.
result These dimensions characterize realizable and agnostic k-list regression.