Spatial-multiplexing cameras have emerged as a promising alternative to classical imaging devices, often enabling acquisition of 'more for less'. One popular architecture for spatial multiplexing is the single-pixel camera (SPC), which acquires coded measurements of the scene with pseudo-random spatial masks. Significant theoretical developments over the past few years provide a means for reconstruction of the original imagery from coded measurements at sub-Nyquist sampling rates. Yet, accurate reconstruction generally requires high measurement rates and high signal-to-noise ratios. In this paper, we enquire if one can perform high-level visual inference problems (e.g. face recognition or action recognition) from compressive cameras without the need for image reconstruction. This is an interesting question since in many practical scenarios, our goals extend beyond image reconstruction. However, most inference tasks often require non-linear features and it is not clear how to extract such features directly from compressed measurements. In this paper, we show that one can extract nontrivial correlational features directly without reconstruction of the imagery. As a specific example, we consider the problem of face recognition beyond the visible spectrum e.g in the short-wave infra-red region (SWIR)-where pixels are expensive. We base our framework on smashed filters which suggests that inner-products between high-dimensional signals can be computed in the compressive domain to a high degree of accuracy. We collect a new face image dataset of 30 subjects, obtained using an SPC. Using face recognition as an example, we show that one can indeed perform reconstruction-free inference with a very small loss of accuracy at very high compression ratios of 100 and more.