Probabilistic Inference in Autonomous Driving

Minjae Kim
University of Yonsei
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Abstract

This project focuses on developing a probabilistic model for road type identification, utilizing Naive Bayes and Bayesian Estimation.

The primary goal is to distingush between different road types based on image data, with a model trained on a set of observed hypotheses. The Naive Bayes Classifier is applied for straightforward classification by calculating the probability of each road type hypothesis given the observed features. In contrast, Bayesian Estimation is used to handle sequential observations, allowing for dynamic state updates and predictions over time.

To enhance model robustness, Laplacian Smoothing is applied to avoid zero-probability issues for unseen observations. Through simulation, I demonstrate the effectiveness of probabilistic inference in accurately identifying road types, which can be applied to improve decision-making processes in autonomous systems.

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Naive Bayes

Using Naive Bayes classification, we can calculate the conditional probability of each road type hypothesis given the observed features.

Bayesian Estimation

Using Bayesian Estimation, sequential observations and dynamically update the system's state, we can predict the road type over time.

Calculation Method

Hypothesis Space

The hypothesis space for different road types, such as

Interpolate start reference image.

Naive Bayes Classification

In the Naive Bayes classification method, we calculate the conditional probability for each road type hypothesis given observed features. By assuming feature independence, we simplify the computation of joint probabilities, allowing efficient classification. For each road type hypothesis \( h \), the probability is computed as follows:

\[ P(h|z) \propto P(h) \prod_{i=1}^{n} P(z_i|h) \]

Here, \( z \) represents the observed features, and \( P(h|z) \) indicates the posterior probability of road type hypothesis \( h \) given these observations. The model selects the hypothesis with the highest posterior probability, effectively classifying the road type.

Bayesian Estimation for State Update

Bayesian Estimation is used to update the system’s state dynamically based on sequential observations. Starting with an initial prior probability distribution for each road type, the model continuously refines its prediction as new data becomes available. The Bayesian update rule is applied as follows:

\[ P(h|z_{1:t}) = \frac{P(z_t|h) \cdot P(h|z_{1:t-1})}{P(z_t|z_{1:t-1})} \]

In this formula, \( z_{1:t} \) represents all observations from time 1 to time \( t \), and \( P(h|z_{1:t}) \) is the updated probability of each hypothesis. This approach enables the model to account for uncertainties and make predictions based on continuously updated information, which is especially useful in dynamic environments like autonomous driving.