Related papers: Group testing and local search: is there a computa…
A variety of information processing tasks in practice involve recovering $n$ objects from single-shot graph-based measurements, particularly those taken over the edges of some measurement graph $\mathcal{G}$. This paper concerns the…
In confirmatory clinical trials with small sample sizes, hypothesis tests based on asymptotic distributions are often not valid and exact non-parametric procedures are applied instead. However, the latter are based on discrete test…
In group testing, simple binary-output tests are designed to identify a small number $t$ of defective items that are present in a large population of $N$ items. Each test takes as input a group of items and produces a binary output…
We study the fundamental tradeoffs between computational tractability and statistical accuracy for a general family of hypothesis testing problems with combinatorial structures. Based upon an oracle model of computation, which captures the…
A method is introduced for approximate marginal likelihood inference via adaptive Gaussian quadrature in mixed models with a single grouping factor. The core technical contribution is an algorithm for computing the exact gradient of the…
The goal of group testing is to efficiently identify a few specific items, called positives, in a large population of items via tests. A test is an action on a subset of items which returns positive if the subset contains at least one…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
Group testing is a useful method that has broad applications in medicine, engineering, and even in airport security control. Consider a finite population of $N$ items, where item $i$ has a probability $p_i$ to be defective. The goal is to…
We derive an information-theoretic lower bound for sample complexity in sparse recovery problems where inputs can be chosen sequentially and adaptively. This lower bound is in terms of a simple mutual information expression and unifies many…
This paper considers the problem of Quantitative Group Testing (QGT) where there are some defective items among a large population of $N$ items. We consider the scenario in which each item is defective with probability $K/N$, independently…
Identification of defective members of large populations has been widely studied in the statistics community under the name of group testing. It involves grouping subsets of items into different pools and detecting defective members based…
In this paper, we introduce a variation of the group testing problem where each test is specified by an ordered subset of items and returns the first defective item in the specified order or returns null if there are no defectives. We refer…
In the context of the phase retrieval problem, it is known that certain natural classes of measurements, such as Fourier measurements and random Bernoulli measurements, do not lead to the unique reconstruction of all possible signals, even…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
Combining test statistics from independent trials or experiments is a popular method of meta-analysis. However, there is very limited theoretical understanding of the power of the combined test, especially in high-dimensional models…
While neural networks have shown remarkable success on classification tasks in terms of average-case performance, they often fail to perform well on certain groups of the data. Such group information may be expensive to obtain; thus, recent…
We consider the quantitative group testing problem where the objective is to identify defective items in a given population based on results of tests performed on subsets of the population. Under the quantitative group testing model, the…
In the long-studied problem of combinatorial group testing, one is asked to detect a set of $k$ defective items out of a population of size $n$, using $m \ll n$ disjunctive measurements. In the non-adaptive setting, the most widely used…
Running machine learning algorithms on large and rapidly growing volumes of data is often computationally expensive, one common trick to reduce the size of a data set, and thus reduce the computational cost of machine learning algorithms,…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…