August 12, 2024
Identifiable VAE (iVAE) [1] is a variant of the Variational Autoencoder (VAE) model with the primary goal of making this model “identifiable.” This means that iVAE ensures that the latent variables \(z\) it learns are unique (up to permutation), unaffected by unwanted transformations such as permutation or nonlinear transformation. Below is a detailed explanation of the structure and functioning of iVAE.
1. Basics of Identifiability in Machine Learning # Identifiability in machine learning refers to the ability to uniquely determine the latent variables \(z\) from the observed data \(x\).
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July 31, 2024
We learn features that enable discriminating data points from different time segments We use ordinary neural network training: Last hidden layer gives the features Surprising theoretical result: Estimates a nonlinear ICA model with general nonlinear mixing $x(t) = f(s(t))$ nonstationary components $s_{i}(t)$
July 26, 2024
Autocorrelation is a concept in statistics and signal processing used to measure the correlation of a signal with itself at different time lags. In other words, autocorrelation determines the similarity of the signal at one time point compared to previous time points.
Formula # The autocorrelation of a signal \( x(t) \) at a time lag \( \tau \) is defined as:
\[ R(\tau) = \mathbb{E}[x(t) \cdot x(t + \tau)] \] Where:
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July 26, 2024
In signal processing, the concepts of stationary and non-stationary are used to describe the properties of a signal over time.
Stationary Signal # A signal is called stationary if its statistical properties do not change over time. These statistical properties include mean, variance, and correlation functions. There are two types of stationarity:
Weak Stationarity (or Wide-Sense Stationarity): The signal has a constant mean and variance over time, and the correlation function depends only on the time difference between two points, not on the specific time points themselves.
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July 25, 2024
July 24, 2024
What is the Motor Imagery ? # Motor imagery is the imagination of specific motor commands, such as left-hand, right-hand, or foot movement, which can modify neuronal activity in primary sensorimotor areas. 1
The neurophysiological basis of motor imagery # “Motor Imagery and Direct Brain–Computer Communication.” GERT PFURTSCHELLER, 2001. ↩︎
July 23, 2024
Khái niệm # Phân tích thành phần độc lập (ICA) là một kỹ thuật thống kê và tính toán được sử dụng trong học máy để tách tín hiệu đa biến thành các thành phần không phải Gaussian độc lập của nó. Mục tiêu của ICA là tìm ra một phép biến đổi tuyến tính của dữ liệu sao cho dữ liệu được chuyển đổi càng gần độc lập về mặt thống kê càng tốt.
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