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The problem of finding an optimum using noisy evaluations of a smooth cost function arises in many contexts, including economics, business, medicine, experiment design, and foraging theory. We derive an asymptotic bound E[ (x_t - x*)^2 ] >=…

We consider the evaluation of first-order queries over classes of databases with bounded expansion. The notion of bounded expansion is fairly broad and generalizes bounded degree, bounded treewidth and exclusion of at least one minor. It…

Recent empirical studies show three phenomena with increasing size of language models: compute-optimal size scaling, emergent capabilities, and performance plateauing. We present a simple unified mathematical framework to explain all of…

Many major works in social science employ matching to make causal conclusions, but different matches on the same data may produce different treatment effect estimates, even when they achieve similar balance or minimize the same loss…

Estimation of individual treatment effects is commonly used as the basis for contextual decision making in fields such as healthcare, education, and economics. However, it is often sufficient for the decision maker to have estimates of…

Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based…

Cardinality estimation (CardEst) still remains a challenging problem for DBMS. Recent years have witnessed the success of ML-based cardinality estimators in outperforming traditional methods. However, these solutions suffer from poor…

Complex event processing (CEP) is a prominent technology used in many modern applications for monitoring and tracking events of interest in massive data streams. CEP engines inspect real-time information flows and attempt to detect…

This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful…

Query containment and query answering are two important computational tasks in databases. While query answering amounts to compute the result of a query over a database, query containment is the problem of checking whether for every…

This paper studies the generalization performance of multi-class classification algorithms, for which we obtain, for the first time, a data-dependent generalization error bound with a logarithmic dependence on the class size, substantially…

We use an entropy based method to study two graph maximization problems. We upper bound the number of matchings of fixed size $\ell$ in a $d$-regular graph on $N$ vertices. For $\frac{2\ell}{N}$ bounded away from 0 and 1, the logarithm of…

Scaling Laws have emerged as a powerful framework for understanding how model performance evolves as they increase in size, providing valuable insights for optimizing computational resources. In the realm of Sequential Recommendation (SR),…

Information theoretic quantities are extremely useful in discovering relationships between two or more data sets. One popular method---particularly for continuous systems---for estimating these quantities is the nearest neighbour…

The goal of this paper is to characterize Gaussian-Process optimization in the setting where the function domain is large relative to the number of admissible function evaluations, i.e., where it is impossible to find the global optimum. We…

Large language models (LLMs) have become essential for applications such as text summarization, sentiment analysis, and automated question-answering. Recently, LLMs have also been integrated into relational database management systems to…

Large language models (LLMs) have been widely adopted due to their remarkable performance across various applications, driving the accelerated development of a large number of diverse models. However, these individual LLMs show limitations…

Large Language Models (LLMs) have made significant progress in assisting users to query databases in natural language. While LLM-based techniques provide state-of-the-art results on many standard benchmarks, their performance significantly…

Existing studies on differential privacy mainly consider aggregation on data sets where each entry corresponds to a particular participant to be protected. In many situations, a user may pose a relational algebra query on a sensitive…

The problem of online checkpointing is a classical problem with numerous applications which had been studied in various forms for almost 50 years. In the simplest version of this problem, a user has to maintain $k$ memorized checkpoints…