To my surprise, ................
To be honest, ...........
To the best of my knowledge, ....
ONLY A NON-TEACHER'S OPINION
(1) My favorite book calls these absolute (independent) constructions. That is,
they do not belong grammatically to the following sentence. (If you deleted
(erased) those absolute/independent constructions, your sentence would still be good
English.) Those absolute constructions are a comment on what follows.
(a) To my surprise, the usually noisy students were quiet today in class.
(i) "To my surprise" is a prepositional phrase used "absolutely" or "independently."
As you can see, it is a shorter (and more dramatic?) way to say "I was surprised that
the usually noisy students were quiet today in class."
(b) To be honest, I do not like him. He is too rude.
(i) As you know, "to be" is an infinitive. So we can say that "to be honest" is an
infinitive phrase being used absolutely or independently. I think that you could also
express that idea like this: I am being honest: I do not like him. (Here is an example
from Descriptive English Grammar by House and Harman: "To tell the truth, I
positively dislike him.")
(c) To the best of my knowledge, I have never seen her before.
(i) As you now know, that is a prepositional phrase. It's a comment on "I have
never seen her before." Grammatically speaking, there is no connection. But as
Pence & Emery remind us in A Grammar of Present-Day English, there is, of course,
a logical connection.
(2) Tom: I hear that you have lost all of your money.
Martha: Yes, I have.
Tom: I'm so sorry.
Martha: Thank you for your concern, but at any rate, I still have my good health.
= Well, I am thankful that I still have my good health.
(3) Mona: How do you like this school?
Joe: Some of the teachers are a bit impatient.
Mona: What about the cafeteria food?
Joe: It's super!
Mona: What about the girls?
Joe: They're really beautiful!''
Mona: Well, it seems to me that, on the whole, you have little to complain about,
dude! = When you consider everything, you have little ....
(Credit goes to Pence & Emery's book for the prepositional phrases "at any rate"
and "on the whole.")