Daniel Csillag

@dccsillag.xyz

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Applied mathematician working on machine learning, statistics and compilers. Currently doing research at FGV EMAp. dccsillag.xyz

Main theorems of our work, establishing marginal and training-conditional guarantees under strategic alterations for our method.
Front page of our paper, 'Strategic Conformal Prediction'. Abstract: When a machine learning model is deployed, its predictions can alter its environment, as better informed agents strategize to suit their own interests. With such alterations in mind, existing approaches to uncertainty quantification break. In this work we propose a new framework, Strategic Conformal Prediction, which is capable of robust uncertainty quantification in such a setting. Strategic Conformal Prediction is backed by a series of theoretical guarantees spanning marginal coverage, training-conditional coverage, tightness and robustness to misspecification that hold in a distribution-free manner. Experimental analysis further validates our method, showing its remarkable effectiveness in face of arbitrary strategic alterations, whereas other methods break.
Let $f : RR^n -> RR$ be twice continuously differentiable and assume its gradient is Lipschitz. Consider gradient descent with random initialization: $ x_0 ~ nn(bold(0),I), wide wide x_(t+1) = x_t - eta nabla f(x_t). $ If the procedure converges to some point $macron(x)$ and $eta$ is sufficiently small, then, almost surely: (i) It is a critical/stationary point: $nabla f(macron(x)) = 0$. (ii) It is a second-order stationary point: the Hessian $nabla^2 f(macron(x))$ is positive-semidefinite. This means that it will not converge to maxima, nor most other spurious stationary points. So, even though GD only uses first-order information (the gradient), we get a second-order guarantee "for free!"