arXiv subjects

Pratik Worah

Publications and source records attributed to Pratik Worah.

14 recordsLinked to original sources

arXiv2026

Conditioned free-energy density of proteins using unbalanced solutions to constraint satisfaction problems

We show that computing the log-partition function (free-energy) of conditioned inhomogeneous Curie--Weiss spin Hamiltonians reduces to an unbalanced $2 \to 1$ norm computation, and design a polynomial-time SDP algorithm for this problem with a lower bound proof for the amount of unbalance achieved. Applied to the protein Ubiquitin, the framework starts from a known crystal structure, explores alternative backbone conformations across the free-energy landscape, and identifies flexible regions of the protein while preserving its native secondary structure.

cs.LG↗

arXiv2025

A Goemans-Williamson type algorithm for identifying subcohorts in clinical trials

We design an efficient algorithm that outputs tests for identifying predominantly homogeneous subcohorts of patients from large in-homogeneous datasets. Our theoretical contribution is a rounding technique, similar to that of Goemans and Wiliamson (1995), that approximates the optimal solution within a factor of $0.82$. As an application, we use our algorithm to trade-off sensitivity for specificity to systematically identify clinically interesting homogeneous subcohorts of patients in the RNA microarray dataset for breast cancer from Curtis et al. (2012). One such clinically interesting subcohort suggests a link between LXR over-expression and BRCA2 and MSH6 methylation levels for patients in that subcohort.

q-bio.QM↗

arXiv2025

Approximating a gene regulatory network from non-sequential data

Given non-sequential snapshots from instances of a dynamical system, we design a compressed sensing based algorithm that reconstructs the dynamical system. On the theoretical side, we show that: (1) successful reconstruction is possible under the assumption that we can construct an approximate clock from a subset of the coordinates of the underlying system, and (2) computing the minimal Lyapunov exponent of the dynamical system, where the minimum is taken over all subsets of coordinates of the dynamical system, equates to computing a min-max equilibrium. We design an efficient randomized algorithm for computing the above equilibrium. As an application of our theoretical results, we reconstruct the underlying dynamical system from publicly available RNA-seq data to: (1) predict the underlying gene regulatory networks (as opposed to individual genes) that may help differentiate between metastatic vs non-metastatic breast cancer (and also colorectal cancer), and (2) identify candidate genes that could be used as target biomarkers for basket trials. In particular, our in silico analysis suggests that RORC agonists, which are already used in colorectal cancer therapies, may be worth investigating for breast cancers.

q-bio.GN↗

arXiv2025

Sampling and Loss Weights in Multi-Domain Training

In the training of large deep neural networks, there is a need for vast amounts of training data. To meet this need, data is collected from multiple domains, such as Wikipedia and GitHub. These domains are heterogeneous in both data quality and the diversity of information they provide. This raises the question of how much we should rely on each domain. Several methods have attempted to address this issue by assigning sampling weights to each data domain using heuristics or approximations. As a first step toward a deeper understanding of the role of data mixing, this work revisits the problem by studying two kinds of weights: sampling weights, which control how much each domain contributes in a batch, and loss weights, which scale the loss from each domain during training. Through a rigorous study of linear regression, we show that these two weights play complementary roles. First, they can reduce the variance of gradient estimates in iterative methods such as stochastic gradient descent (SGD). Second, they can improve generalization performance by reducing the generalization gap. We provide both theoretical and empirical support for these claims. We further study the joint dynamics of sampling weights and loss weights, examining how they can be combined to capture both contributions.

cs.LG↗

arXiv2025

LAVA: Lifetime-Aware VM Allocation with Learned Distributions and Adaptation to Mispredictions

Scheduling virtual machines (VMs) on hosts in cloud data centers dictates efficiency and is an NP-hard problem with incomplete information. Prior work improved VM scheduling with predicted VM lifetimes. Our work further improves lifetime-aware scheduling using repredictions with lifetime distributions versus one-shot prediction. Our approach repredicts and adjusts VM and host lifetimes when incorrect predictions emerge. We also present novel approaches for defragmentation and regular system maintenance, which are essential to our data center reliability and optimizations, and are not explored in prior work. We show repredictions deliver a fundamental advance in effectiveness over one-shot prediction. We call our novel combination of distribution-based lifetime predictions and scheduling algorithms Lifetime Aware VM Allocation (LAVA). LAVA reduces resource stranding and increases the number of empty hosts, which are critical for large VM scheduling, cloud system updates, and reducing dynamic energy consumption. Our approach runs in production within Google's hyperscale cloud data centers, where it improves efficiency by decreasing stranded compute and memory resources by ~3% and ~2% respectively. It increases empty hosts by 2.3-9.2 pp in production, reducing dynamic energy consumption, and increasing availability for large VMs and cloud system updates. We also show a reduction in VM migrations for host defragmentation and maintenance. In addition to our fleet-wide production deployment, we perform simulation studies to characterize the design space and show that our algorithm significantly outperforms the prior state of the art lifetime-based scheduling approach.

cs.DC↗

arXiv2025

Enhancing selectivity using Wasserstein distance based reweighing

Given two labeled data-sets $\mathcal{S}$ and $\mathcal{T}$, we design a simple and efficient greedy algorithm to reweigh the loss function such that the limiting distribution of the neural network weights that result from training on $\mathcal{S}$ approaches the limiting distribution that would have resulted by training on $\mathcal{T}$. On the theoretical side, we prove that when the metric entropy of the input datasets is bounded, our greedy algorithm outputs a close to optimal reweighing, i.e., the two invariant distributions of network weights will be provably close in total variation distance. Moreover, the algorithm is simple and scalable, and we prove bounds on the efficiency of the algorithm as well. As a motivating application, we train a neural net to recognize small molecule binders to MNK2 (a MAP Kinase, responsible for cell signaling) which are non-binders to MNK1 (a highly similar protein). In our example dataset, of the 43 distinct small molecules predicted to be most selective from the enamine catalog, 2 small molecules were experimentally verified to be selective, i.e., they reduced the enzyme activity of MNK2 below 50\% but not MNK1, at 10$μ$M -- a 5\% success rate.

stat.ML↗

arXiv2025

Allocating Variance to Maximize Expectation

We design efficient approximation algorithms for maximizing the expectation of the supremum of families of Gaussian random variables. In particular, let $\mathrm{OPT}:=\max_{σ_1,\cdots,σ_n}\mathbb{E}\left[\sum_{j=1}^{m}\max_{i\in S_j} X_i\right]$, where $X_i$ are Gaussian, $S_j\subset[n]$ and $\sum_iσ_i^2=1$, then our theoretical results include: - We characterize the optimal variance allocation -- it concentrates on a small subset of variables as $|S_j|$ increases, - A polynomial time approximation scheme (PTAS) for computing $\mathrm{OPT}$ when $m=1$, and - An $O(\log n)$ approximation algorithm for computing $\mathrm{OPT}$ for general $m>1$. Such expectation maximization problems occur in diverse applications, ranging from utility maximization in auctions markets to learning mixture models in quantitative genetics.

cs.LG↗

arXiv2023

Learning Rate Schedules in the Presence of Distribution Shift

We design learning rate schedules that minimize regret for SGD-based online learning in the presence of a changing data distribution. We fully characterize the optimal learning rate schedule for online linear regression via a novel analysis with stochastic differential equations. For general convex loss functions, we propose new learning rate schedules that are robust to distribution shift and we give upper and lower bounds for the regret that only differ by constants. For non-convex loss functions, we define a notion of regret based on the gradient norm of the estimated models and propose a learning schedule that minimizes an upper bound on the total expected regret. Intuitively, one expects changing loss landscapes to require more exploration, and we confirm that optimal learning rate schedules typically increase in the presence of distribution shift. Finally, we provide experiments for high-dimensional regression models and neural networks to illustrate these learning rate schedules and their cumulative regret.

cs.LG↗

arXiv2023

Description Complexity of Regular Distributions

Myerson's regularity condition of a distribution is a standard assumption in economics. In this paper, we study the complexity of describing a regular distribution within a small statistical distance. Our main result is that $\tildeΘ{(ε^{-0.5})}$ bits are necessary and sufficient to describe a regular distribution with support $[0,1]$ within $ε$ Levy distance. We prove this by showing that we can learn the regular distribution approximately with $\tilde{O}(ε^{-0.5})$ queries to the cumulative density function. As a corollary, we show that the pricing query complexity to learn the class of regular distribution with support $[0,1]$ within $ε$ Levy distance is $\tildeΘ{(ε^{-2.5})}$. To learn the mixture of two regular distributions, $\tildeΘ(ε^{-3})$ pricing queries are required.

cs.GT↗

arXiv2021

Pricing Query Complexity of Revenue Maximization

The common way to optimize auction and pricing systems is to set aside a small fraction of the traffic to run experiments. This leads to the question: how can we learn the most with the smallest amount of data? For truthful auctions, this is the \emph{sample complexity} problem. For posted price auctions, we no longer have access to samples. Instead, the algorithm is allowed to choose a price $p_t$; then for a fresh sample $v_t \sim \mathcal{D}$ we learn the sign $s_t = sign(p_t - v_t) \in \{-1,+1\}$. How many pricing queries are needed to estimate a given parameter of the underlying distribution? We give tight upper and lower bounds on the number of pricing queries required to find an approximately optimal reserve price for general, regular and MHR distributions. Interestingly, for regular distributions, the pricing query and sample complexities match. But for general and MHR distributions, we show a strict separation between them. All known results on sample complexity for revenue optimization follow from a variant of using the optimal reserve price of the empirical distribution. In the pricing query complexity setting, we show that learning the entire distribution within an error of $ε$ in Levy distance requires strictly more pricing queries than to estimate the reserve. Instead, our algorithm uses a new property we identify called \emph{relative flatness} to quickly zoom into the right region of the distribution to get the optimal pricing query complexity.

cs.GT↗

arXiv2021

Learning to Price Against a Moving Target

In the Learning to Price setting, a seller posts prices over time with the goal of maximizing revenue while learning the buyer's valuation. This problem is very well understood when values are stationary (fixed or iid). Here we study the problem where the buyer's value is a moving target, i.e., they change over time either by a stochastic process or adversarially with bounded variation. In either case, we provide matching upper and lower bounds on the optimal revenue loss. Since the target is moving, any information learned soon becomes out-dated, which forces the algorithms to keep switching between exploring and exploiting phases.

cs.GT↗

arXiv2021

The Landscape of the Proximal Point Method for Nonconvex-Nonconcave Minimax Optimization

Minimax optimization has become a central tool in machine learning with applications in robust optimization, reinforcement learning, GANs, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify and deal with the fundamental difficulties this poses. In this paper, we study the classic proximal point method (PPM) applied to nonconvex-nonconcave minimax problems. We find that a classic generalization of the Moreau envelope by Attouch and Wets provides key insights. Critically, we show this envelope not only smooths the objective but can convexify and concavify it based on the level of interaction present between the minimizing and maximizing variables. From this, we identify three distinct regions of nonconvex-nonconcave problems. When interaction is sufficiently strong, we derive global linear convergence guarantees. Conversely when the interaction is fairly weak, we derive local linear convergence guarantees with a proper initialization. Between these two settings, we show that PPM may diverge or converge to a limit cycle.

math.OC↗

arXiv2021

Limiting Behaviors of Nonconvex-Nonconcave Minimax Optimization via Continuous-Time Systems

Unlike nonconvex optimization, where gradient descent is guaranteed to converge to a local optimizer, algorithms for nonconvex-nonconcave minimax optimization can have topologically different solution paths: sometimes converging to a solution, sometimes never converging and instead following a limit cycle, and sometimes diverging. In this paper, we study the limiting behaviors of three classic minimax algorithms: gradient descent ascent (GDA), alternating gradient descent ascent (AGDA), and the extragradient method (EGM). Numerically, we observe that all of these limiting behaviors can arise in Generative Adversarial Networks (GAN) training and are easily demonstrated for a range of GAN problems. To explain these different behaviors, we study the high-order resolution continuous-time dynamics that correspond to each algorithm, which results in the sufficient (and almost necessary) conditions for the local convergence by each method. Moreover, this ODE perspective allows us to characterize the phase transition between these different limiting behaviors caused by introducing regularization as Hopf Bifurcations.

math.OC↗

arXiv2013

A Characterization of Approximation Resistance

A predicate f:{-1,1}^k -> {0,1} with ρ(f) = \frac{|f^{-1}(1)|}{2^k} is called {\it approximation resistant} if given a near-satisfiable instance of CSP(f), it is computationally hard to find an assignment that satisfies at least ρ(f)+Ω(1) fraction of the constraints. We present a complete characterization of approximation resistant predicates under the Unique Games Conjecture. We also present characterizations in the {\it mixed} linear and semi-definite programming hierarchy and the Sherali-Adams linear programming hierarchy. In the former case, the characterization coincides with the one based on UGC. Each of the two characterizations is in terms of existence of a probability measure with certain symmetry properties on a natural convex polytope associated with the predicate.

cs.CC↗