Let's say that there's some asset traded on an exchange and that, for this asset, I have access to a snapshot of the limit order book (price level and quantity for bids and offers) and subsequent updates to the order book of this asset allowing me to reconstruct an approximation to the order book at a point in time as well as trades as they occur. For simplicity, let us also assume that there aren't any hidden orders or other complicating factors.

Is there a common way to combine the streams of order book and trade data into something more homogeneous?

Since in one direction, the trades do hold important information about the order book such as allowing us to determine when a change in the quantity at price level of the order book is likely due to orders being matched or order cancellation and I can't think of an example, but I'm assuming the converse holds as well for information content.

Also, on a related note, in the context of market-taking, are constructs such as the mid price, micro price, etc. all just different ways of distilling the limit order book into a more(?) tractable form and is coming up with these constructs and modeling them so as to inform trading one of the goals of high frequency market-taking?

Let's say that there's some asset traded on an exchange and that, for this asset, I have access to a snapshot of the limit order book (price level and quantity for bids and offers) and subsequent updates to the order book of this asset allowing me to reconstruct an approximation to the order book at a point in time as well as trades as they occur. For simplicity, let us also assume that there aren't any hidden orders or other complicating factors.

Is there a common way to combine the streams of order book and trade data into something more homogeneous?

Since in one direction, the trades do hold important information about the order book such as allowing us to determine when a change in the quantity at price level of the order book is likely due to orders being matched or order cancellation and I can't think of an example, but I'm assuming the converse holds as well for information content.

Also, on a related note, what are some of examples of the target variable that a high frequency market-taker may try to model/forecast to trade upon? Are these just things such as the mid and micro price + a potential "spread" with any more informative constructions likely being proprietary?