We study the fundamental question of how informative a dataset is for solving a given decision-making task. In our setting, the dataset provides partial information about unknown parameters that influence task outcomes. Focusing on linear programs, we characterize when a dataset is sufficient to recover an optimal decision, given an uncertainty set on the cost vector. Our main contribution is a sharp geometric characterization that identifies the directions of the cost vector that matter for optimality, relative to the task constraints and uncertainty set. We further develop a practical algorithm that, for a given task, constructs a minimal or least-costly sufficient dataset. Our results reveal that small, well-chosen datasets can often fully determine optimal decisions--offering a principled foundation for task-aware data selection.

Neural Information Processing Systems http://nips.cc/

Unsupervised learning of structured predictors has been a long standing pursuit in machine learning. Recently a conditional random field auto-encoder has been proposed in a two-layer setting, allowing latent structured representation to be automatically inferred. Aside from being nonconvex, it also requires the demanding inference of normalization. In this paper, we develop a convex relaxation of two-layer conditional model which captures latent structure and estimates model parameters, jointly and optimally. We further expand its applicability by resorting to a weaker form of inference--maximum a-posteriori. The flexibility of the model is demonstrated on two structures based on total unimodularity--graph matching and linear chain. Experimental results confirm the promise of the method.

Neural Information Processing Systems http://nips.cc/

Z that represents some transfer of mass between elements of w and v . The proof is the same for W . Proposition 2. Suppose that the target row and column representative distributions are the same, The the Kantorovich OT problem and whose rank is at most min(rank(Z), rank( W)) . Proof of proposition 2. From linear algebra, we have that Proof of proposition 3. We suppose that The optimal transport problem can be formulated and solved as the Earth Mover's Distance (EMD) We report the biclustering performance on the synthetic datasets in table 2. At least one of our models finds the perfect partition in all cases. The gene-expression matrices used are the Cumida Breast Cancer and Leukemia datasets. Their characteristics are shown in Table 3. Table 3: Characteristics of the gene expression datasets.

We prove that the corresponding information-theoretic universal rate-distortionperception function is operationally achievable in an approximate sense.