= High-dimensional statistics
<High-dimensional statistics> studies inference when the number of variables or parameters is large relative to the number of observations, often allowing both to grow. The difficulty is structural rather than merely computational: with an $n\times p$ <design matrix> and $p>n$, the <null space> is nontrivial, so $X\beta=X(\beta+v)$ for every $v$ in that <null space>.
The data alone then cannot identify an arbitrary coefficient vector. Assuming a <sparse vector> of <regression coefficients> can make restricted recovery possible when the <design matrix> is injective on the allowed differences. <Regularization> encodes or exploits such structural assumptions. A fitted model with many parameters is therefore not automatically informative about every parameter; <identifiability> and uncertainty depend on the model's structure and sampling design.
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