Related papers: Sequential Mode Estimation with Oracle Queries
Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies $U_tO_x\cdots U_1O_xU_0$ to some input state,…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
Given a sequence of random variables ${\bf X}=X_1,X_2,\ldots$ suppose the aim is to maximize one's return by picking a `favorable' $X_i$. Obviously, the expected payoff crucially depends on the information at hand. An optimally informed…
Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard…
In-context learning (ICL) enables large language models to perform new tasks by conditioning on a sequence of examples. Most prior work reasonably and intuitively assumes that which examples are chosen has a far greater effect on…
We prove that it is NP-hard to properly PAC learn decision trees with queries, resolving a longstanding open problem in learning theory (Bshouty 1993; Guijarro-Lavin-Raghavan 1999; Mehta-Raghavan 2002; Feldman 2016). While there has been a…
We consider the problem of collaborative personalized mean estimation under a privacy constraint in an environment of several agents continuously receiving data according to arbitrary unknown agent-specific distributions. In particular, we…
The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to…
We propose a novel approach to select the best model of the data. Based on the exclusive properties of the nested models, we find the most parsimonious model containing the risk minimizer predictor. We prove the existence of probable…
Contextual bandit algorithms are ubiquitous tools for active sequential experimentation in healthcare and the tech industry. They involve online learning algorithms that adaptively learn policies over time to map observed contexts $X_t$ to…
Given an implicit $n\times n$ matrix $A$ with oracle access $x^TA x$ for any $x\in \mathbb{R}^n$, we study the query complexity of randomized algorithms for estimating the trace of the matrix. This problem has many applications in quantum…
We study the query complexity of quantum learning problems in which the oracles form a group $G$ of unitary matrices. In the simplest case, one wishes to identify the oracle, and we find a description of the optimal success probability of a…
This paper investigates learning-augmented algorithms for smooth integer programs, covering canonical problems such as MAX-CUT and MAX-k-SAT. We introduce a framework that incorporates a predictive oracle to construct a linear surrogate of…
This paper presents generalized probabilistic models for high-order projective dependency parsing and an algorithmic framework for learning these statistical models involving dependency trees. Partition functions and marginals for…
Noise-tolerant PAC learning of linear models has been of central interests in machine learning community since the last century. In recent years, many computationally-efficient algorithms have been proposed for the problem of learning…
Online sequence prediction is the problem of predicting the next element of a sequence given previous elements. This problem has been extensively studied in the context of individual sequence prediction, where no prior assumptions are made…
We investigate the sample complexity of learning the optimal arm for multi-task bandit problems. Arms consist of two components: one that is shared across tasks (that we call representation) and one that is task-specific (that we call…
We introduce the problem of simultaneously learning all powers of a Poisson Binomial Distribution (PBD). A PBD of order $n$ is the distribution of a sum of $n$ mutually independent Bernoulli random variables $X_i$, where $\mathbb{E}[X_i] =…
We study oracle complexity of gradient based methods for stochastic approximation problems. Though in many settings optimal algorithms and tight lower bounds are known for such problems, these optimal algorithms do not achieve the best…
Predictive clustering trees (PCTs) are a well established generalization of standard decision trees, which can be used to solve a variety of predictive modeling tasks, including structured output prediction. Combining them into ensembles…