This research provides theoretical guarantees for hyperparameter estimation in complex network dynamical systems.
problem Theoretical guarantees for hyperparameter estimation in large, inhomogeneous complex network dynamical systems.
method Formulating the system's evolution in a measure transport perspective, proposing a theoretical framework for estimating hyperparameters with mean-type observations.
result A nonasymptotic bound for the deviation of hyperparameter estimates in inhomogeneous complex network dynamical systems with respect to network population size.
We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for several copula families such as the Gaussian copula, copulas of a class of Gaussian mi…
The paper develops a deep neural network estimator for weakly dependent processes with various loss functions.
problem Learning weakly dependent processes with a broad class of loss functions.
method Sparse-penalized deep neural networks with ψ-weak dependence structure and θ∞-coefficients. result Oracle inequalities for the excess risk of the sparse-penalized deep neural networks estimators.
Deep neural nets learn from weakly dependent processes.
problem Learning from ψ-weakly dependent processes. method Deep neural networks for ψ-weakly dependent processes. result Established consistency of empirical risk minimization algorithm and generalization bound.
Low-rank tensor decomposition and completion have attracted significant interest from academia given the ubiquity of tensor data. However, the low-rank structure is a global property, which will not be fulfilled when the data presents complex and weak dependencies given specific graph structures. One particular applica…
The paper bounds the excess risk of deep neural networks for weakly dependent processes.
problem Learning with weakly dependent data using deep neural networks.
method Approximation of smooth functions by deep neural networks and a bound on excess risk.
result The excess risk bound for deep learning under weak dependence is close to O(n−1/2) for sufficiently smooth functions. Paper tackles robust deep learning from weakly dependent data with unbounded loss and input.
problem Tackles robust deep learning from weakly dependent data with unbounded loss and input.
method Establishes non-asymptotic bounds for expected excess risk under strong mixing and ψ-weak dependence assumptions. result Derives a relationship between bounds and r, and shows convergence rate close to i.i.d. results for r=∞. There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive model…
Sparse-penalized deep neural networks improve performance in weakly dependent processes.
problem Nonparametric regression and classification under weak dependence.
method Sparse-penalized deep neural networks with oracle inequalities and convergence rates established.
result The proposed estimators outperform non-penalized ones in simulations.
We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in the asymptotical regime the error upper bounds for the broad …
In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts. In contrast to the Normal- Hedge bound, which mainly depends on the effective number of experts but also weakly depends on the nominal…
Using non-linear machine learning methods and a proper backtest procedure, we critically examine the claim that Google Trends can predict future price returns. We first review the many potential biases that may influence backtests with this kind of data positively, the choice of keywords being by far the greatest culpr…
In this paper, we propose a new framework to study the generalization property of classifier chains trained over observations associated with multiple and interdependent class labels. The results are based on large deviation inequalities for Lipschitz functions of weakly dependent sequences proposed by Rio in 2000. We …
A computationally simple genome-wide association study (GWAS) algorithm for estimating the main and epistatic effects of markers or single nucleotide polymorphisms (SNPs) is proposed. It is based on the intuitive assumption that changes of alleles corresponding to important SNPs in a pair of individuals lead to large d…
In this paper, we consider a model called CHARME (Conditional Heteroscedastic Autoregressive Mixture of Experts), a class of generalized mixture of nonlinear nonparametric AR-ARCH time series. Under certain Lipschitz-type conditions on the autoregressive and volatility functions, we prove that this model is stationary,…
The reparameterization gradient has become a widely used method to obtain Monte Carlo gradients to optimize the variational objective. However, this technique does not easily apply to commonly used distributions such as beta or gamma without further approximations, and most practical applications of the reparameterizat…
Study differentially private methods for learning Hawkes processes.
problem Lack of thorough analysis on sample complexity for learning Hawkes processes parameters and releasing differentially private versions.
method Developed non-private and differentially private estimators for Hawkes processes parameters.
result Obtained sample complexity results for both private and non-private settings.
We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, test…
Bayesian test assesses dependence between mixed data types.
problem Assessing dependence between text, image, and sound data.
method Bayesian kernelised correlation test using Dirichlet process model.
result Demonstrated effectiveness compared to other methods.
We study several aspects of the so-called low-vol and low-beta anomalies, some already documented (such as the universality of the effect over different geographical zones), others hitherto not clearly discussed in the literature. Our most significant message is that the low-vol anomaly is the result of two independent…
The relationship between the size and the variance of firm growth rates is known to follow an approximate power-law behavior σ(S)∼S−β(S) where S is the firm size and β(S)≈0.2 is an exponent weakly dependent on S. Here we show how a model of proportional growth which treats firms as classes compos…
Paper improves generalization bounds for structured output prediction problems.
problem Large label sets in structured output prediction problems.
method Developed novel high-probability bounds and generalization bounds in expectation.
result Significantly improved generalization bounds with logarithmic dependency on label set size.
The architecture of Transformer is based entirely on self-attention, and has been shown to outperform models that employ recurrence on sequence transduction tasks such as machine translation. The superior performance of Transformer has been attributed to propagating signals over shorter distances, between positions in …
LC-GNN improves GNNs for node classification by incorporating label consistency.
problem Limited performance of GNNs due to label consistency assumption not always holding.
method LC-GNN uses node pairs with the same label but unconnected to expand GNN's receptive field.
result LC-GNN outperforms traditional GNNs in semi-supervised node classification.
New AI-block models for clustering high-dimensional variables based on maxima of random processes.
problem Clustering high-dimensional variables with weakly dependent maxima of random processes.
method Asymptotic Independent block (AI-block) models and an algorithm for variable clustering.
result The proposed AI-block models and algorithm can effectively identify clusters in high-dimensional data.
Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an autoencoder-based neural network architecture. The main advantages of the proposed Dee…
Network embedding has proved extremely useful in a variety of network analysis tasks such as node classification, link prediction, and network visualization. Almost all the existing network embedding methods learn to map the node IDs to their corresponding node embeddings. This design principle, however, hinders the ex…
In this work, we address semi-supervised classification of graph data, where the categories of those unlabeled nodes are inferred from labeled nodes as well as graph structures. Recent works often solve this problem via advanced graph convolution in a conventionally supervised manner, but the performance could degrade …
Effectively capturing graph node sequences in the form of vector embeddings is critical to many applications. We achieve this by (i) first learning vector embeddings of single graph nodes and (ii) then composing them to compactly represent node sequences. Specifically, we propose SENSE-S (Semantically Enhanced Node Seq…
Embedding graph nodes into a vector space can allow the use of machine learning to e.g. predict node classes, but the study of node embedding algorithms is immature compared to the natural language processing field because of a diverse nature of graphs. We examine the performance of node embedding algorithms with respe…
Statistical learning theory has largely focused on learning and generalization given independent and identically distributed (i.i.d.) samples. Motivated by applications involving time-series data, there has been a growing literature on learning and generalization in settings where data is sampled from an ergodic proces…
Graph structured data provide two-fold information: graph structures and node attributes. Numerous graph-based algorithms rely on both information to achieve success in supervised tasks, such as node classification and link prediction. However, node attributes could be missing or incomplete, which significantly deterio…
SANNE model generates embeddings for unseen nodes in graph networks.
problem Lack of embeddings for unseen nodes in graph networks.
method SANNE uses a transformer self-attention network to generate embeddings.
result SANNE achieves state-of-the-art results for node classification.
Study finds significant instability in node embeddings due to randomness.
problem Stability of node embeddings under random variations.
method Evaluated five node embedding algorithms (HOPE, LINE, node2vec, SDNE, GraphSAGE) on synthetic and empirical graphs.
result Significant instability in embedding spaces and downstream task accuracy.
We discuss the pricing methodology for Bonus Certificates and Barrier Reverse-Convertible Structured Products. Pricing for a European barrier condition is straightforward for products of both types and depends on an efficient interpolation of observed market option pricing. Pricing products We discuss the pricing metho…
CatGCN improves GCNs by modeling feature interactions for categorical node features.
problem Suboptimal initial node representations in GCNs due to lack of feature interaction modeling.
method Integrates explicit interaction modeling (local and global) into initial node representation learning for categorical node features.
result CatGCN enhances initial node representations through feature interaction modeling, leading to improved model performance.
LASLA improves multiple testing accuracy with network-structured data.
problem Efficiently incorporating complex side information into multiple testing.
method Locally adaptive structure learning algorithm (LASLA) integrating auxiliary information.
result LASLA asymptotically controls FDR and enhances power with side information.
This paper studies node embeddings of networks, revealing their geometric properties.
problem Understanding the geometric properties of node embeddings in random networks.
method Characterization of ergodic limits, generalization, and convex relaxations of random walk node embedding objectives.
result The optimal node embedding Grammians have rank 1 for a nuclear norm relaxation of the non-randomized objective.
This paper assesses tail risk and systemic risk in cryptocurrencies using expectiles and MES.
problem Quantifying tail risk and systemic risk in cryptocurrencies.
method The study uses expectiles and Marginal Expected Shortfall (MES) to assess tail risk and systemic risk of cryptocurrencies.
result The expectile-based approach and MES provide a dynamic method to evaluate the impact of single assets on systemic risk.
Paper proves impossibility of three desirable properties in node embedding.
problem Understanding limitations of node embedding methods.
method Axiomatic approach to node embedding, proving impossibility of three properties.
result No node embedding method can satisfy all three desirable properties simultaneously.
Learning node embeddings that capture a node's position within the broader graph structure is crucial for many prediction tasks on graphs. However, existing Graph Neural Network (GNN) architectures have limited power in capturing the position/location of a given node with respect to all other nodes of the graph. Here w…
GraphCL learns node representations by maximizing similarity between perturbed node features.
problem Learning node representations in graph data without labeled data.
method Contrastive learning of node embeddings using graph neural networks and a loss function.
result Significantly outperforms state-of-the-art in unsupervised node classification benchmarks.
ARGEW improves node embeddings for weighted homophilous graphs by emphasizing strong edge weights.
problem Lack of accurate node embeddings for weighted homophilous graphs.
method ARGEW (Augmentation of Random walks by Graph Edge Weights) augments random walks by emphasizing nodes with larger edge weights.
result ARGEW produces embeddings where node pairs with strong edge weights have closer embeddings.
Basel II and Solvency 2 both use the Value-at-Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log returns of financial assets. This is usually justified by the use of the Central Limi…
SPARC tackles cold-start nodes in graphs by using spectral embeddings.
problem Cold-start nodes in graphs lacking initial connections.
method Introduces SPARC, a framework utilizing spectral embeddings to predict on cold-start nodes.
result SPARC outperforms existing models on cold-start nodes across tasks.
Knowledge representation of graph-based systems is fundamental across many disciplines. To date, most existing methods for representation learning primarily focus on networks with simplex labels, yet real-world objects (nodes) are inherently complex in nature and often contain rich semantics or labels, e.g., a user may…
SIGNNAP learns stable and identifiable node representations in GNNs against graph perturbations.
problem Fragility of GNN models to graph perturbations leading to unreliable node representations.
method SIGNNAP proposes a novel model that learns stable and identifiable node representations in an unsupervised manner, formalizing stability and identifiability through a contrastive objective and preserving smoothness with existing GNN backbones.
result SIGNNAP demonstrates effectiveness in learning stable and identifiable node representations in GNNs against graph perturbations on six benchmarks.
PanRep learns universal node embeddings for heterogeneous graphs.
problem Learning universal node embeddings for heterogeneous graphs.
method Graph Neural Network (GNN) model with four decoders capturing different properties.
result PanRep outperforms unsupervised and supervised methods in node classification and link prediction.