A/B testing is critical for modern technological companies to evaluate the effectiveness of newly developed products against standard baselines. This paper studies optimal designs that aim to maximize the amount of information obtained from online experiments to estimate treatment effects accurately.

We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural reconstruction model and a fixed-budget set of continuous design variables representing sensor locations, sampling times, or measurement angles, within a single optimization loop. By optimizing measurement locations directly rather than weighting a dense grid of candidates, the proposed approach enforces sparsity by design, eliminates the need for l1 tuning, and substantially reduces computational complexity. We validate NODE on an analytically tractable exponential growth benchmark, on MNIST image sampling, and illustrate its effectiveness on a real world sparse view X ray CT example. In all cases, NODE outperforms baseline approaches, demonstrating improved reconstruction accuracy and task-specific performance.

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Humans (and many vertebrates) face the problem of fusing together multiple fixations of a scene in order to obtain a representation of the whole, where each fixation uses a high-resolution fovea and decreasing resolution in the periphery. In this paper we explicitly represent the retinal transformation of a fixation as a linear downsampling of a high-resolution latent image of the scene, exploiting the known geometry. This linear transformation allows us to carry out exact inference for the latent variables in factor analysis (FA) and mixtures of FA models of the scene. Further, this allows us to formulate and solve the choice of "where to look next" as a Bayesian experimental design problem using the Expected Information Gain criterion. Experiments on the Frey faces and MNIST datasets demonstrate the effectiveness of our models.

In A.1, we show consequence of Def. 1 which is used in the proofs We can apply Theorem??, to get C We show that our condition in Def. 1 and Pukelsheims and estimability This definition is sometimes used as restatement of the estimability property. Definition 4 (Projected data) . Lemma 2. The assumption in Definition 4 implies the assumption in Definition 1 with This section includes proofs for the concentration results presented in the main text. Z is as in Def. 2 where X The term above is so called self-normalized noise, which can be handled by techniques of de la Peña et al. (2009) popularized by Abbasi-Y adkori et al. (2011). From now on the proof is generic.

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In A.1, we show consequence of Def. 1 which is used in the proofs We can apply Theorem??, to get C We show that our condition in Def. 1 and Pukelsheims and estimability This definition is sometimes used as restatement of the estimability property. Definition 4 (Projected data) . Lemma 2. The assumption in Definition 4 implies the assumption in Definition 1 with This section includes proofs for the concentration results presented in the main text. Z is as in Def. 2 where X The term above is so called self-normalized noise, which can be handled by techniques of de la Peña et al. (2009) popularized by Abbasi-Y adkori et al. (2011). From now on the proof is generic.