# A Short Note on Concentration Inequalities for Random Vectors with SubGaussian Norm

arXiv: https://arxiv.org/abs/1902.03736 · HTML: https://mlsanity.com/paper/1902.03736/

## Key facts

- Cited by 106 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2019.

## Built on by (most cited first, 30 of 106)

- [Learning with User-Level Privacy](https://mlsanity.com/paper/2102.11845/) (2021)
- [Minibatch optimal transport distances; analysis and applications](https://mlsanity.com/paper/2101.01792/) (2021)
- [Learning time-scales in two-layers neural networks](https://mlsanity.com/paper/2303.00055/) (2023)
- [Generalization in Graph Neural Networks: Improved PAC-Bayesian Bounds on Graph Diffusion](https://mlsanity.com/paper/2302.04451/) (2023)
- [Robust Fine-Tuning of Deep Neural Networks with Hessian-based Generalization Guarantees](https://mlsanity.com/paper/2206.02659/) (2022)
- [Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior](https://mlsanity.com/paper/2307.14619/) (2023)
- [Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments](https://mlsanity.com/paper/2204.08281/) (2022)
- [Faster Rates of Convergence to Stationary Points in Differentially Private Optimization](https://mlsanity.com/paper/2206.00846/) (2022)
- [Robust Policy Gradient against Strong Data Corruption](https://mlsanity.com/paper/2102.05800/) (2021)
- [A Simple Reward-free Approach to Constrained Reinforcement Learning](https://mlsanity.com/paper/2107.05216/) (2021)
- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [Concentration of Contractive Stochastic Approximation: Additive and Multiplicative Noise](https://mlsanity.com/paper/2303.15740/) (2023)
- [Nonlinear spiked covariance matrices and signal propagation in deep neural networks](https://mlsanity.com/paper/2402.10127/) (2024)
- [Neural Estimation of Statistical Divergences](https://mlsanity.com/paper/2110.03652/) (2021)
- [A Free Lunch from the Noise: Provable and Practical Exploration for Representation Learning](https://mlsanity.com/paper/2111.11485/) (2021)
- [Improved Convergence of Score-Based Diffusion Models via Prediction-Correction](https://mlsanity.com/paper/2305.14164/) (2023)
- [On the Provable Advantage of Unsupervised Pretraining](https://mlsanity.com/paper/2303.01566/) (2023)
- [Adapting to Function Difficulty and Growth Conditions in Private Optimization](https://mlsanity.com/paper/2108.02391/) (2021)
- [Corruption Robust Offline Reinforcement Learning with Human Feedback](https://mlsanity.com/paper/2402.06734/) (2024)
- [Locally Private k-Means in One Round](https://mlsanity.com/paper/2104.09734/) (2021)
- [Improved Regret Bound and Experience Replay in Regularized Policy Iteration](https://mlsanity.com/paper/2102.12611/) (2021)
- [Embed to Control Partially Observed Systems: Representation Learning with Provable Sample Efficiency](https://mlsanity.com/paper/2205.13476/) (2022)
- [Nest Your Adaptive Algorithm for Parameter-Agnostic Nonconvex Minimax Optimization](https://mlsanity.com/paper/2206.00743/) (2022)
- [Efficient Model-Free Exploration in Low-Rank MDPs](https://mlsanity.com/paper/2307.03997/) (2023)
- [Stochastic Optimization under Distributional Drift](https://mlsanity.com/paper/2108.07356/) (2021)
- [Information Complexity of Stochastic Convex Optimization: Applications to Generalization and Memorization](https://mlsanity.com/paper/2402.09327/) (2024)
- [Locally Differentially Private Reinforcement Learning for Linear Mixture Markov Decision Processes](https://mlsanity.com/paper/2110.10133/) (2021)
- [Faster Differentially Private Convex Optimization via Second-Order Methods](https://mlsanity.com/paper/2305.13209/) (2023)
- [Projection-Free Methods for Stochastic Simple Bilevel Optimization with Convex Lower-level Problem](https://mlsanity.com/paper/2308.07536/) (2023)
- [Tuning-Free Stochastic Optimization](https://mlsanity.com/paper/2402.07793/) (2024)

## Abstract (arXiv)

In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.
