What if we can use diffusion models to generate Laproscopic surgeries to train surgeons?

Problem

Asking dalle to just “generate a Laproscopic surgery” is not going to work. It will give you cartoons.

Approach

1. text problem formulation: “grasper grasp gallbladder”
2. encode text into latents
3. do diffusion with late fusion of latents

Data: Cholec T-45

Weighting

Scoring: Perception Prioritized Weighting + Prioritization for Signal-to-Noise

(Ho et al, 2020)

Text

“[subject] [verb] [object] [surgical phase]”

The dimension of a vector space is the length of any basis in the vector space. It is denoted as \(\dim V\).

additional information

See also finite-dimensional vector space and infinite-demensional vector space

dimension of subspace is smaller or equal to that of its parent

If we have a finite-dimensional \(V\) and a subspace thereof \(U\), then \(\dim U \leq \dim V\).

Firstly, the every subspace of a finite-dimensional vector space is a finite-dimensional vector space is itself a finite-dimensional vector space. Therefore, it has a finite dimension.

direct estimation of the probability of failure:

1. perform a rollout of the system
2. label the outcome as \(1\) if the trajectory is a failure, and \(0\) otherwise

this is just Direct Sampling.

From there, we can just go about estimating this using standard parameter estimation (i.e. using MLE estimation or Baysian estimation.)

maximum-likelihood estimation of failure distribution

\begin{equation} \hat{p}_{\text{fail}} = \frac{1}{m} \sum_{i=1}^{m} 1\qty {\tau_{i} \not \in \psi} = \frac{n}{m} \end{equation}

for \(n\) failures and \(m\) rollouts, where \(\tau \sim p\qty(\cdot)\).

Direct Sampling is the act in probability to sample what you want from the distribution. This is often used when actual inference impossible. It involves. well. sampling from the distribution to compute a conditional probability that you want.

It basically involves invoking the Frequentist Definition of Probability without letting \(n \to \infty\), instead just sampling some \(n < \infty\) and dividing the event space by your sample space.

So, for instance, to compute inference on \(b^{1}\) given observations \(d^{1}c^{1}\), we can write: