The paper introduces walks with jumps for modeling neuron activity in hyperbolic space.
problem Encoding neuron activity sequences in hyperbolic space.
method Introducing walks with jumps in hyperbolic geometry to model neuron activity.
result Endpoints of walks with jumps do not fully encode the sequence of jump times.
Efficiently identifies users from walking activity data using kernel-based DTW.
problem Identifying users from walking activity data streams.
method Learning a kernel to approximate DTW for efficient analysis of streaming data from wearable sensors.
result The proposed approach reduces computational burden compared to traditional DTW.
We present results from a set of experiments in this pilot study to investigate the causal influence of user activity on various environmental parameters monitored by occupant carried multi-purpose sensors. Hypotheses with respect to each type of measurements are verified, including temperature, humidity, and light lev…
Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random walks to develop a spectral theory for hypergraphs with edge-dependent vertex wei…
Proposes a new model for time series that considers smooth transitions between states.
problem Models assume instantaneous transitions between discrete states, ignoring gradual changes.
method Dynamical Wasserstein Barycentric (DWB) model that estimates system state and pure state distributions over time.
result Accurately learns pure state distributions and improves state estimation for transition periods.
Community detection has been an active research area for decades. Among all probabilistic models, Stochastic Block Model has been the most popular one. This paper introduces a novel probabilistic model: RW-HDP, based on random walks and Hierarchical Dirichlet Process, for community extraction. In RW-HDP, random walks c…
This paper studies how AMMs can minimize losses from arbitrage while retaining uninformed trading activity.
problem Minimizing losses from arbitrage in AMMs while retaining uninformed trading activity.
method Modeling arbitrage dynamics and sensitivity to fee choices, mapping to a random walk with a reward scheme.
result AMMs can maximize value retention by optimizing fee structures.
We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between `active' and `inactive' strategies is subordinated to random-walk like processes. We numerically demonstrate our scenario in the fr…
RW-based learning is vulnerable to the Pac-Man attack, which eliminates active RWs.
problem Vulnerability of RW-based learning to malicious behavior.
method Proposed the Average Crossing (AC) algorithm to prevent RW extinction.
result RW-based stochastic gradient descent remains convergent under AC, even in the presence of Pac-Man.
The paper tackles uniform sampling from neural networks efficiently.
problem Uniform sampling from neural network labelings given a sample.
method Polynomial-time algorithm for general neural networks, random walk for single neuron.
result Uniform sampling with high probability for general neural networks, exact uniform sampling for single neuron.
This paper extends geometric study of neural networks to non-differentiable layers and random walks.
problem Understanding the geometric properties of neural networks, especially those with non-differentiable activation functions.
method Singular Riemannian geometry approach to convolutional, residual, and recursive neural networks.
result Illustrated geometric findings with numerical experiments on image classification and thermodynamic problems.
TG-GAN models dynamic graph evolution for continuous-time temporal graphs.
problem Challenges in modeling dynamic temporal graphs, especially in continuous time.
method Temporal Graph Generative Adversarial Network (TG-GAN) that models truncated edge sequences, time budgets, and node attributes.
result TG-GAN significantly outperforms existing methods in efficiency and effectiveness.
A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion coefficient is proportional to the activity. It is formulated as a generalization o…
Model place cells as spatial embeddings for efficient path planning and cognitive map construction.
problem Encoding spatial navigation in the hippocampus.
method Model place cells using spectral decomposition of multi-step random walk transition kernels, inducing sparsity and adjacency.
result Place cells encode spatial information through non-negativity and inner-product structure, forming a cognitive map.
Researchers use information geometry to analyze and improve DRWs for node classification.
problem Lack of theoretical foundations for Discriminative Random Walks (DRWs).
method Revisit DRWs through information geometry, treating hitting-time laws as a statistical manifold. Derived closed-form expressions and introduced sensitivity scores.
result Introduced a sensitivity score that bounds maximal first-order change in DRW betweenness under unit Fisher perturbations.
A novel unified Bayesian framework for network detection is developed, under which a detection algorithm is derived based on random walks on graphs. The algorithm detects threat networks using partial observations of their activity, and is proved to be optimum in the Neyman-Pearson sense. The algorithm is defined by a …
HHAR-net uses neural networks to recognize human activities at different levels of abstraction.
problem Recognizing different layers of human activities concealed in behavior.
method Hierarchical classification with Neural Networks.
result 95.8% accuracy for low-level activities and 92.8% overall accuracy.
As part of daily monitoring of human activities, wearable sensors and devices are becoming increasingly popular sources of data. With the advent of smartphones equipped with acceloremeter, gyroscope and camera; it is now possible to develop activity classification platforms everyone can use conveniently. In this paper,…
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in the case of the Grover walk on lattices. Moreover, our numerical simulation sugge…
Contextual policy search allows adapting robotic movement primitives to different situations. For instance, a locomotion primitive might be adapted to different terrain inclinations or desired walking speeds. Such an adaptation is often achievable by modifying a small number of hyperparameters. However, learning, when …
Automates feature extraction for IMU-based activity recognition.
problem Manual feature engineering is time-consuming and limits IMU-based applications.
method FRESH algorithm for automated feature extraction.
result Workflow automates feature extraction from synchronized IMU sensors.
New hypergraph method improves scRNA-seq clustering.
problem Loss of higher-order information and overestimation in coexpression networks.
method Conceptualizing scRNA-seq data as hypergraphs and proposing novel clustering methods.
result Proposed methods outperform existing methods on simulated and real datasets.
New graph embedding method uses domain-specific knowledge.
problem Lack of semantic information in existing graph embedding approaches.
method Domain-aware biased random walks to incorporate semantic information.
result Embeddings achieve equal or greater accuracy than domain-independent methods.
This paper presents VEC-NBT, a variation on the unsupervised graph clustering technique VEC, which improves upon the performance of the original algorithm significantly for sparse graphs. VEC employs a novel application of the state-of-the-art word2vec model to embed a graph in Euclidean space via random walks on the n…
We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and the John walk, for generating samples from the uniform distribution over a polytope. Both random walks are sampling algorithms derived from interior point methods. The former is based on volumetric-logarithmic barrier introduced by Vaidya wher…
Study large deviations in random walks on Lie groups.
problem Large deviations in sub-Riemannian random walks.
method Prove large deviation principle for random walks on stratified Lie groups.
result Proved a large deviation principle with a rate function adapted to sub-Riemannian geometry.
Quantum walks blend patterns into splines when averaged.
problem Understanding the asymptotic patterns of quantum random walks.
method Averaging over quantum coins using the Haar measure.
result Patterns blend into splines, showing a unified behavior.
Unified view on random walk and Weisfeiler-Leman kernels, improving accuracy.
problem Improving graph kernel methods for better classification accuracy.
method Define and analyze walk-based node refinement methods, relate to Weisfeiler-Leman test, and introduce new walk-based kernels.
result Walk-based kernels are as expressive as Weisfeiler-Leman subtree kernel but support non-strict neighborhood comparison.
We analyse the dependence of stock return cross-correlations on the sampling frequency of the data known as the Epps effect: For high resolution data the cross-correlations are significantly smaller than their asymptotic value as observed on daily data. The former description implies that changing trading frequency sho…
Local limit theorem for random walks on hyperbolic groups with parabolic subgroups.
problem Analyzing the behavior of random walks on relatively hyperbolic groups.
method Study of convergent random walks with finite derivative of Green function at spectral radius.
result Proves a local limit theorem for the probability of returning to the origin.
We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few…
Study random walks on sub-Riemannian manifolds using retractions.
problem Modeling random walks on sub-Riemannian manifolds.
method Use retractions to approximate normal geodesics and study convergence to Brownian motion.
result Convergence of geodesic random walks defined with different connections.
Random walks on cell complexes link to Laplacians and Novikov-Shubin invariants.
problem Computing Novikov-Shubin invariants for complex cell structures.
method Construct random walks on cell complexes, relate to Laplacians, and use return probabilities.
result Novikov-Shubin invariants can be recovered from random walk return probabilities.
Study diffusions and random walks on hyperbolic spaces, focusing on their Martin boundaries.
problem Understanding diffusions and random walks on hyperbolic spaces.
method Analyzing specific diffusions and random walks on hyperbolic spaces, examining their Martin boundaries.
result Characterized the Martin boundaries of diffusions and random walks on hyperbolic spaces.
This paper investigates the scaling dependencies between measures of "activity" and of "size" for companies included in the FTSE 100. The "size" of companies is measured by the total market capitalization. The "activity" is measured with several quantities related to trades (transaction value per trade, transaction val…
New proof shows rapid mixing for random walks on nilmanifolds.
problem Proving rapid mixing for random walks on nilmanifolds.
method Proved rapid mixing for almost all random walks generated by m translations on nilmanifolds under mild assumptions.
result For several classical classes of nilmanifolds, m=2 suffices for rapid mixing.
The paper finds braid representatives minimizing simple walks for knots.
problem Finding efficient braid representatives for knots.
method Developed methods to minimize the number of simple walks in braids.
result Computed the colored Jones polynomial for specific knots.
Quantum walks model financial returns with flexibility and asymmetry.
problem Accurate modeling of financial asset price dynamics.
method Discrete-time quantum walks to model asset price evolution.
result Quantum walk models can generate asymmetric return distributions and higher probabilities for extreme events.
Random walks on metric spaces embed quasi-isometrically into the space.
problem Embedding random subgroups of metric spaces quasi-isometrically.
method Analyzing random walks and contracting elements in metric spaces.
result Random subgroups of isometry groups are quasi-isometrically embedded.
Study random walks on groups with superlinear divergent geodesics.
problem Existence of superlinear divergent geodesics in groups.
method Developed theory of superlinear divergence and applied Gouëzel's pivoting technique.
result Established a central limit theorem for random walks on groups with superlinear divergent geodesics.
This work investigates how context should be taken into account when performing continuous authentication of a smartphone user based on touchscreen and accelerometer readings extracted from swipe gestures. The study is conducted on the publicly available HMOG dataset consisting of 100 study subjects performing pre-defi…
New walk extraction strategies improve node embeddings in KGs.
problem Improving node embeddings in knowledge graphs.
method Proposed five different walk extraction strategies to complement basic random walks.
result The n-gram strategy performs best on average for node classification tasks.
A new method for embedding heterogeneous networks using spacey random walks.
problem Stationarity issues in meta-path guided random walks for HIN embedding.
method Heterogeneous personalized spacey random walk.
result Substantial improvement over existing network embedding algorithms.
A scalable framework preserves personalized higher-order network proximities.
problem Lack of expressive methods to preserve personalized higher-order network proximities.
method Incorporates random walk into a sound objective to preserve arbitrary higher-order proximities and introduces random walk with restart for personalized-weighted preservation.
result Consistently and substantially outperforms state-of-the-art methods on real-world networks.
Random walks on hyperbolic spaces show linear growth in translation lengths.
problem Investigate the growth of translation lengths in random walks on hyperbolic spaces.
method Prove linear growth without moment conditions and apply to Teichmüller spaces.
result Linear growth of translation lengths in random walks on hyperbolic spaces.
Geodesic walks converge to Brownian motion on Finsler manifolds.
problem Understanding random walks on Finsler manifolds.
method Analyzing convergence of geodesic random walks to diffusion processes.
result The Brownian motion on a Riemannian metric is a key result.
The paper examines random walks on metric spaces and finds commensurable subgroups.
problem Determining commensurable subgroups via stationary measures in metric spaces.
method Analyzing random walks on isometry groups of metric spaces with non-singular stationary measures.
result Subgroups generated by random walks are commensurable under mild conditions.
Random walks on free groups reveal asymmetric expansion factors.
problem Understanding expansion factors in free groups.
method Random walks and BGIP on metric spaces.
result Generic outer automorphisms have different forward and backward expansion factors.