in spite of, nevertheless, although, despite, no matter the, regardless of
Noun / な-Adjective +
Used to express that an action or event occurs despite a state involving a noun or な-adjective. While nouns can attach directly to the grammar point, な-adjectives must be followed by a state modifier like なの or である.
Noun + (なの / である / だった) +
Nouns can attach directly to the grammar point to set a simple condition, or they can take a modifier like なの, である, or their past tense forms to emphasize being in that state.
雨
Despite the rain, I went outside.
子供なの
In spite of being a child, they read the newspaper.
な-Adjective + なの / である / だった +
な-Adjectives cannot attach directly to this grammar point. You must always add a modifier like なの, である, or だった to the adjective stem.
危険なの
Despite it being dangerous, I will climb the mountain.
元気だった
In spite of having been healthy, they took a day off school.
The main difference between these two is that omitting the state modifier for a noun is perfectly fine, but doing so for a な-adjective is ungrammatical. Using modifiers like なの or である with nouns adds a slight nuance of stating a factual contradiction.
Verb / い-Adjective (Informal) +
Used to indicate that an unexpected outcome happens in spite of the action or state described by a verb or an い-adjective. Both parts of speech use their informal forms and behave identically here.
Verb (Informal) + (の) +
Shows that a present or past action is contradicted by the outcome. The nominalizer の can optionally be added between the verb and the grammar point.
毎日走る
Despite running every day, I do not lose weight.
たくさん寝たの
In spite of having slept a lot, I am sleepy.
い-Adjective (Informal) + (の) +
Expresses a situation that occurs despite the present or past state of the い-adjective. Just like with verbs, the nominalizer の is optional.
高い
Despite being expensive, I bought a watch.
寒かったの
In spite of it having been cold, I swam.
Adding the optional の nominalizes the preceding verb or adjective clause, making it function more like a noun phrase. Both constructions (with or without の) are completely grammatical and have mostly the same meaning, though の is more common for spoken Japanese.