arXiv subjects

Andrew Tan

Publications and source records attributed to Andrew Tan.

5 recordsLinked to original sources

arXiv2025

The Labeled Coupon Collector Problem

We generalize the well-known Coupon Collector Problem (CCP) in combinatorics. Our problem is to find the minimum and expected number of draws, with replacement, required to recover $n$ distinctly labeled coupons, with each draw consisting of a random subset of $k$ different coupons and a random ordering of their associated labels. We specify two variations of the problem, Type-I in which the set of labels is known at the start, and Type-II in which the set of labels is unknown at the start. We show that our problem can be viewed as an extension of the separating system problem introduced by R\'enyi and Katona, provide a full characterization of the minimum, and provide a numerical approach to finding the expectation using a Markov chain model, with special attention given to the case where two coupons are drawn at a time.

cs.DM↗

arXiv2020

AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically being orders of magnitude more robust toward noise and bad data, and also by discovering many formulas that stumped previous methods. We develop a method for discovering generalized symmetries (arbitrary modularity in the computational graph of a formula) from gradient properties of a neural network fit. We use normalizing flows to generalize our symbolic regression method to probability distributions from which we only have samples, and employ statistical hypothesis testing to accelerate robust brute-force search.

cs.LG↗

arXiv2020

Approximating Boolean Functions with Disjunctive Normal Form

The theorem states that: Every Boolean function can be $\epsilon -approximated$ by a Disjunctive Normal Form (DNF) of size $O_{\epsilon}(2^{n}/\log{n})$. This paper will demonstrate this theorem in detail by showing how this theorem is generated and proving its correctness. We will also dive into some specific Boolean functions and explore how these Boolean functions can be approximated by a DNF whose size is within the universal bound $O_{\epsilon}(2^{n}/\log{n})$. The Boolean functions we interested in are: Parity Function: the parity function can be $\epsilon-approximated$ by a DNF of width $(1 - 2\epsilon)n$ and size $2^{(1 - 2\epsilon)n}$. Furthermore, we will explore the lower bounds on the DNF's size and width. Majority Function: for every constant $1/2 < \epsilon < 1$, there is a DNF of size $2^{O(\sqrt{n})}$ that can $\epsilon-approximated$ the Majority Function on n bits. Monotone Functions: every monotone function f can be $\epsilon-approximated$ by a DNF g of size $2^{n - \Omega\epsilon(n)}$ satisfying $g(x) \le f(x)$ for all x.

cs.CC↗

arXiv2019

Can multimodal sensing detect and localize transient events?

With the increased focus on making cities "smarter", we see an upsurge in investment in sensing technologies embedded in the urban infrastructure. The deployment of GPS sensors aboard taxis and buses, smartcards replacing paper tickets, and other similar initiatives have led to an abundance of data on human mobility, generated at scale and available real-time. Further still, users of social media platforms such as Twitter and LBSNs continue to voluntarily share multimedia content revealing in-situ information on their respective localities. The availability of such longitudinal multimodal data not only allows for both the characterization of the dynamics of the city, but also, in detecting anomalies, resulting from events (e.g., concerts) that disrupt such dynamics, transiently. In this work, we investigate the capabilities of such urban sensor modalities, both physical and social, in detecting a variety of local events of varying intensities (e.g., concerts) using statistical outlier detection techniques. We look at loading levels on arriving bus stops, telecommunication records, and taxi trips, accrued via the public APIs made available through the local transport authorities from Singapore and New York City, and Twitter/Foursquare check-ins collected during the same period, and evaluate against a set of events assimilated from multiple event websites. In particular, we report on our early findings on (1) the spatial impact evident via each modality (i.e., how far from the event venue is the anomaly still present), and (2) the utility in combining decisions from the collection of sensors using rudimentary fusion techniques.

eess.SP↗

arXiv2017

Sentiment Predictability for Stocks

In this work, we present our findings and experiments for stock-market prediction using various textual sentiment analysis tools, such as mood analysis and event extraction, as well as prediction models, such as LSTMs and specific convolutional architectures.

cs.CL↗