Related papers: Optimal Rate-Exponent Region for a Class of Hypoth…
We study the error exponents in quantum hypothesis testing between two sets of quantum states, extending the analysis beyond the independent and identically distributed case to encompass composite correlated hypotheses. In particular, we…
Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much…
In the problem of asymptotic binary i.i.d. state discrimination, the optimal asymptotics of the type I and the type II error probabilities is in general an exponential decrease to zero as a function of the number of samples; the set of…
A detection system with a single sensor and $\mathsf{K}$ detectors is considered, where each of the terminals observes a memoryless source sequence and the sensor sends a common message to all the detectors. The communication of this…
In this paper, we study the problem of relaying a single bit over a tandem of binary-input channels, with the goal of attaining the highest possible error exponent in the exponentially decaying error probability. Our previous work gave an…
We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error…
Consider the problem of distributed binary hypothesis testing with two terminals, where the decision is made at one of them (the "receiver"). We study the exponent of the error probability of the second type. Previously, an achievable…
The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…
Constraint based causal structure learning for point processes require empirical tests of local independence. Existing tests require strong model assumptions, e.g. that the true data generating model is a Hawkes process with no latent…
Marton's optimal error exponent for the lossy source coding problem is defined as a non-convex optimization problem. This fact had prevented us to develop an efficient algorithm to compute it. This problem is caused by the fact that the…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
The problem of distributed representation learning is one in which multiple sources of information $X_1,\ldots,X_K$ are processed separately so as to learn as much information as possible about some ground truth $Y$. We investigate this…
We study the optimal rates of convergence for estimating a prior distribution over a VC class from a sequence of independent data sets respectively labeled by independent target functions sampled from the prior. We specifically derive upper…
We study adversarial binary hypothesis testing under memory constraints. The test is a time-invariant randomized finite state machine (FSM) with S states. Associated with each hypothesis is a set of distributions. Given the hypothesis, the…
This paper studies model checking for general parametric regression models having no dimension reduction structures on the predictor vector. Using any U-statistic type test as an initial test, this paper combines the sample-splitting and…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
We consider the problem of modulation and estimation of a random parameter $U$ to be conveyed across a discrete memoryless channel. Upper and lower bounds are derived for the best achievable exponential decay rate of a general moment of the…
In this work, we revisit outlier hypothesis testing and propose exponentially consistent, low-complexity fixed-length tests that achieve a better tradeoff between detection performance and computational complexity than existing…
We consider the discrete memoryless degraded broadcast channels with feedback. We prove that the error probability of decoding tends to one exponentially for rates outside the capacity region and derive an explicit lower bound of this…
Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized…