The Limitations of Optimization from Samples

In this paper we consider the following question: can we optimize objective functions from the training data we use to learn them? We formalize this question through a novel framework we call optimization from samples (OPS). In OPS, we are given sampled values of a function drawn from some distribution and the objective is to optimize the function under some constraint. While there are interesting classes of functions that can be optimized from samples, our main result is an impossibility. We show that there are classes of functions which are statistically learnable and optimizable, but for which no reasonable approximation for optimization from samples is achievable. In particular, our main result shows that there is no constant factor approximation for maximizing coverage functions under a cardinality constraint using polynomially-many samples drawn from any distribution. We also show tight approximation guarantees for maximization under a cardinality constraint of several interesting classes of functions including unit-demand, additive, and general monotone submodular functions, as well as a constant factor approximation for monotone submodular functions with bounded curvature

A disposable bio-nano-chip usuing agarose beads for protein analysis

This thesis reports on the fabrication of a disposable bio-nano-chip (BNC), a microfluidic device composed of polydimethylsiloxane (PDMS) and thiolene-based optical epoxy which is both cost-effective and suitable for high performance immunoassays. A novel room temperature (RT) bonding technique was utilized so as to achieve irreversible covalent bonding between PDMS and thiolene-based epoxy layers, while at the same time being compatible with the insertion of agarose bead sensors, selectively arranged in an array of pyramidal microcavities replicated in the thiolene thin film layer. In the sealed device, the bead-supporting epoxy film is sandwiched between two PDMS layers comprising of fluidic injection and drain channels. The agarose bead sensors used in the device are sensitized with anti-C-reactive protein (CRP) antibody, and a fluorescent sandwich-type immunoassay was run to characterize the performance of this device. Computational fluid dynamics (CFD) was used based on the device specifications to model the bead penetration. Experimental data revealed analyte penetration of the immunocomplex to 100μm into the 280μm diameter agarose beads, which correlated well with the simulation. A dose response curve was obtained and the linear dynamic range of the assay was established over 1ng/mL to 50ng/mL with a limit of detection less than 1ng/mL

Shaping Social Activity by Incentivizing Users

Events in an online social network can be categorized roughly into endogenous events, where users just respond to the actions of their neighbors within the network, or exogenous events, where users take actions due to drives external to the network. How much external drive should be provided to each user, such that the network activity can be steered towards a target state? In this paper, we model social events using multivariate Hawkes processes, which can capture both endogenous and exogenous event intensities, and derive a time dependent linear relation between the intensity of exogenous events and the overall network activity. Exploiting this connection, we develop a convex optimization framework for determining the required level of external drive in order for the network to reach a desired activity level. We experimented with event data gathered from Twitter, and show that our method can steer the activity of the network more accurately than alternatives