In this paper we consider a version of the zero-shot learning problem where seen class source and target domain data are provided. The goal during test-time is to accurately predict the class label of an unseen target domain instance based on revealed source domain side information (e.g. attributes) for unseen classes. Our method is based on viewing each source or target data as a mixture of seen class proportions and we postulate that the mixture patterns have to be similar if the two instances belong to the same unseen class. This perspective leads us to learning source/target embedding functions that map an arbitrary source/target domain data into a same semantic space where similarity can be readily measured. We develop a max-margin framework to learn these similarity functions and jointly optimize parameters by means of cross validation. Our test results are compelling, leading to significant improvement in terms of accuracy on most benchmark datasets for zero-shot recognition.

The fundamental task of group testing is to recover a small distinguished subset of items from a large population while efficiently reducing the total number of tests (measurements). The key contribution of this paper is in adopting a new information-theoretic perspective on group testing problems. We formulate the group testing problem as a channel coding/decoding problem and derive a single-letter characterization for the total number of tests used to identify the defective set. Although the focus of this paper is primarily on group testing, our main result is generally applicable to other compressive sensing models.The single letter characterization is shown to be order-wise tight for many interesting noisy group testing scenarios. Specifically, we consider an additive Bernoulli(q) noise model where we show that, for N items and K defectives, the number of tests T is O K log N 1−q for arbitrarily small average error probability and O K 2 log N 1−q for a worst case error criterion. We also consider dilution effects whereby a defective item in a positive pool might get diluted with probability u and potentially missed. In this case, it is shown that T is Ofor the average and the worst case error criteria, respectively. Furthermore, our bounds allow us to verify existing known bounds for noiseless group testing including the deterministic noise-free case and approximate reconstruction with bounded distortion. Our proof of achievability is based on random coding and the analysis of a Maximum Likelihood Detector, and our information theoretic lower bound is based on Fano's inequality.

Zero-shot recognition (ZSR) deals with the problem of predicting class labels for target domain instances based on source domain side information (e.g. attributes) of unseen classes. We formulate ZSR as a binary prediction problem. Our resulting classifier is class-independent. It takes an arbitrary pair of source and target domain instances as input and predicts whether or not they come from the same class, i.e. whether there is a match. We model the posterior probability of a match since it is a sufficient statistic and propose a latent probabilistic model in this context. We develop a joint discriminative learning framework based on dictionary learning to jointly learn the parameters of our model for both domains, which ultimately leads to our class-independent classifier. Many of the existing embedding methods can be viewed as special cases of our probabilistic model. On ZSR our method shows 4.90% improvement over the state-of-the-art in accuracy averaged across four benchmark datasets. We also adapt ZSR method for zero-shot retrieval and show 22.45% improvement accordingly in mean average precision (mAP).

We consider the problem of detecting a small subset of defective items from a large set via non-adaptive "random pooling" group tests. We consider both the case when the measurements are noiseless, and the case2 when the measurements are noisy (the outcome of each group test may be independently faulty with probability q). Order-optimal results for these scenarios are known in the literature. We give information-theoretic lower bounds on the query complexity of these problems, and provide corresponding computationally efficient algorithms that match the lower bounds up to a constant factor. To the best of our knowledge this work is the first to explicitly estimate such a constant that characterizes the gap between the upper and lower bounds for these problems.

In this paper we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy projections. We consider two settings: output noise models where the noise enters after the projection and input noise models where the noise enters before the projection. We consider two types of distortion for reconstruction: support errors and mean-squared errors. Our goal is to relate the number of measurements, m, and SNR, to signal sparsity, k, distortion level, d, and signal dimension, n.We consider support errors in a worst-case setting. We employ different variations of Fano's inequality to derive necessary conditions on the number of measurements and SNR required for exact reconstruction. To derive sufficient conditions we develop new insights on max-likelihood analysis based on a novel superposition property. In particular this property implies that small support errors are the dominant error events. Consequently, our ML analysis does not suffer the conservatism of the union bound and leads to a tighter analysis of max-likelihood. These results provide order-wise tight bounds. For output noise models we show that asymptotically an SNR of Θ(log(n)) together with Θ(k log(n/k)) measurements is necessary and sufficient for exact support recovery. Furthermore, if a small fraction of support errors can be tolerated, a constant SNR turns out to be sufficient in the linear sparsity regime. In contrast for input noise models we show that support recovery fails if the number of measurements scales as o(n log(n)/SN R) implying poor compression performance for such cases.Motivated by the fact that the worst-case setup requires significantly high SNR and substantial number of measurements for input and output noise models, we consider a Bayesian setup. To derive necessary conditions we develop novel extensions to Fano's inequality to handle continuous domains and arbitrary distortions. We then develop a new max-likelihood analysis over the set of rate distortion quantization points to characterize tradeoffs between mean-squared distortion and the number of measurements using rate-distortion theory. We show that with constant SNR the number of measurements scales linearly with the rate-distortion function of the sparse phenomena.