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We present a new adaptive algorithm for learning discrete distributions under distribution drift. In this setting, we observe a sequence of independent samples from a discrete distribution that is changing over time, and the goal is to…
We study the computational complexity of approximately computing the partition function of a spin system. Techniques based on standard counting-to-sampling reductions yield $\tilde{O}(n^2)$-time algorithms, where $n$ is the size of the…
The efficient preparation of input distributions is an important problem in obtaining quantum advantage in a wide range of domains. We propose a novel quantum algorithm for the efficient preparation of arbitrary normal distributions in…
Speculative Decoding has gained popularity as an effective technique for accelerating the auto-regressive inference process of Large Language Models. However, Speculative Decoding entirely relies on the availability of efficient draft…
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,…
Data selection is essential for training deep learning models. An effective data sampler assigns proper sampling probability for training data and helps the model converge to a good local minimum with high performance. Previous studies in…
We present a sublinear randomized algorithm to compute a sparse Fourier transform for nonequispaced data. Suppose a signal S is known to consist of N equispaced samples, of which only L<N are available. If the ratio p=L/N is not close to 1,…
We present efficient algorithms to generate a bit string in which each bit is set with arbitrary probability. By adopting a hybrid algorithm, i.e., a finite-bit density approximation with correction techniques, we achieve 3.8 times faster…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…
We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of average fidelity of a quantum logic gate acting on a d-dimensional system using much fewer random bits than what was known so far. Previous…
We propose a simple algorithm for generating normally distributed pseudo random numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and…
Many applications, including natural language processing, sensor networks, collaborative filtering, and federated learning, call for estimating discrete distributions from data collected in batches, some of which may be untrustworthy,…
SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…
The use of fluorescent molecules to create long sequences of low-density, diffraction-limited images enables highly-precise molecule localization. However, this methodology requires lengthy imaging times, which limits the ability to view…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
Probability estimation is an elementary building block of every statistical data compression algorithm. In practice probability estimation is often based on relative letter frequencies which get scaled down, when their sum is too large.…
In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the degree to which RF automatically adapts to the intrinsic…
We present and implement the concept of the Fourier-domain dedispersion (FDD) algorithm, a brute-force incoherent dedispersion algorithm. This algorithm corrects the frequency-dependent dispersion delays in the arrival time of radio…
Discrete diffusion language models improve generation efficiency through parallel token prediction, but standard $X_0$ prediction methods introduce factorization errors by approximating the clean token posterior with independent token-wise…