Cross Entropy Method is a “conditional MLE” objective; whereby we try to maximize:

• the log prob
• of the true y labels in the training data
• given the observations

Derivation

Recall the Bernoulli distribution, and specifically:

\begin{equation} P(Y=y) = p^{y} (1-p)^{1-y} \end{equation}

Meaning, we want to maximize:

\begin{equation} \log P(y=y) = y \log p + (1-y)\log (1-y) \end{equation}

specifically, we’d like to minimize:

\begin{equation} -[y \log p + (1-y)\log (1-y)] \end{equation}

Intuition

This function should be

This method introduces a search distribution instead of discrete points:

\begin{equation} p(\theta | \psi) \end{equation}

We want to know how parameters \(\theta\) are distributed, given some input parameters \(\psi\) (for instance, we assume parameters are gaussian distributed such as the mean/variance).

1. Given this distribution, we sample \(m\) samples of \(\theta\) from the distribution. Those are our starting candidate points.
2. We then check its policy for its utility via the Roll-out utility
3. We want to take top \(k\) of our best performers, called “elite samples” \(m_{elite}\)
4. Use the set of \(m_{elite}\) points, we fit a new distribution parameter \(\psi\) that describes those sample

This allows us to bound how many Roll-out utilities we are doing.

constituents

additional information

lack of inverse of cross product

The cross product doesn’t have an inverse

geometric interpretation of cross product

\begin{equation} a \times b = |\vec{a}| |\vec{b}| \sin \theta n \end{equation}

where, \(n\) is the unit vector in some direction.

The length of the resulting vector in the cross product is the area of the parallelogram formed by the two vectors.

CrossFinder is a darkpool owned by Credit Suisse.

Features:

1. Normal darkpooling
2. Routing the transaction out to other exchanges and dark-pools if needed
3. Measuring the latency of each other exchange, etc.

cyro-EM is a structure determination system of a solution (Dutta, M. 2018. J indian inst sci 98) to analyze a structural population of particles from TEM; the resulting 3-D structures obtained can be analyzed and classified.

“The Resolution Revolution”: much better structures to analyze because of high-fidelity cyro-EM

cyro-EM vs x-ray crystallography

cyro-EM can identify heterogeneous motions throughout the structure, instead of averaging out multiple structural combinations; instead of the “general” structure on average, we can get a collection of various states the particle can be in.