E[tr(X)]=tr(E[X])인 이유
가 random matrix이다. 성립한다. 왜?
확률론
확률론에 대해 알려드릴게요.
Instantaneous Change of Variables Formula와 그 증명
아래와 같은 미분방정식이 있다. 의 분포를 라고 하자. 그러면 아래를 만족하고 이것을 Instantaneous change of variables formula리 한다. 위의 식에서 입력변수가 stochastic process 로써 는 에 관한 함수로 간주된다. 증명을 해보자. 라는 사실과 log continuity equation을 이용하면! 지금까지 했던것은 Neura ode와 연관있고 neural ode는 flow matching과 관계 있고 flow matching의 응용으로 음성향상에 쓰인 FlowSE [1]가 … Read more
log continuity equation을 증명하자.
아래와 같은 continuity equation이 있다고 하자. 위의 식을 좀더 전개해보자. 이므로 이것을 contiuity equation에 대입하자. 그러면 이것을 로 나누자. 이것을 다시 정리하면 아래의 논문을 이해하는데 큰 자산이 될것이다. References [1] Lee, S., Cheong, S., Han, S., & Shin, J. W. FlowSE: Flow Matching-based Speech Enhancement. ICASSP 2025. doi:10.1109/ICASSP49660.2025.10888274.
[논문리뷰세미나] Score-Based Generative Modeling through Stochastic Differential Equations
[발표자료_1]이성규_Score-based generative modeling through stochastic differential equations [발표자료_2]이성규_Score-based generative modeling through stochastic differential equations [발표자료_3]이성규_Score-based generative modeling through stochastic differential equations
[논문리뷰세미나] Evidential Deep Learning to Quantify Classification Uncertainty
[논문리뷰세미나] Evidential Deep Learning to Quantify Classification Uncertainty [pdf] 이성규_Evidential Deep Learning to Quantify Classification Uncertainty.pdf [ppt] 이성규_Evidential Deep Learning to Quantify Classification Uncertainty.pptx
[논문리뷰] Denoising Diffusion Probabilistic Models
[논문리뷰] Denoising Diffusion Probabilistic Models 논문 리뷰 해봤습니다. [ppt] [발표자료.`22.12.02]이성규_DDPM
Perturbation kernels in diffusion models.
In this post, I will introduce perturbation kernels in diffusion models. Before reading this post, I recommend reading my previous posts. Reverse SDE in diffusion models Denoising score matching loss in diffusion models Score model in diffusion models Score function of a stochastic process Forward stochastic differential equation (SDE) Forward SDE describes a process where … Read more
Score model in diffusion models
In this post, I will introduce the score model in diffusion models. I recommend reading my previous posts before proceedings. Reverse SDE in diffusion models Score function of a stochastic process Reverse stochastic differential equation (SDE) In diffusion models, data samples are generated by integrating reverse SDE: where is the score function of . Score … Read more
Score function of a stochastic process
In this post, I will introduce the score function of a stochastic process. Before proceeding, I recommend that reading my previous posts below Score function of a random vector stochastic process, random process, 랜덤프로세스, 확률과정의 정의 Stochastic process A stochastic process is a collection of random vectors . For each time index , is a … Read more
Score function of a random vector
In this post, I will introduce the score function of a random vector. Let be a random vector with a probability density function (pdf) Definition of score function The score function of the random vector is defined as the gradient of log of its pdf: