arXiv subjects

Rajat Sen

Publications and source records attributed to Rajat Sen.

At least 19 recordsLinked to original sources

arXiv2026

Rethinking Multimodal Time-Series Forecasting Evaluation

We introduce a new context-enriched, multimodal time series forecasting benchmark, TimesX. TimesX contains a wide selection of high-quality real-world time series with diverse domains and textual contexts obtained from an automated data generation pipeline, which helps address three main issues of existing multimodal forecasting benchmarks: (1) poor generalization due to the small scale and synthetic nature of benchmark data, (2) very limited types of textual contexts in the benchmarks, and (3) an inability to mitigate data leakage in evaluation. We conduct a thorough empirical study of zero-shot multimodal forecasting approaches on TimesX. Our results suggest that many approaches that perform well on existing benchmarks may fail on TimesX. In contrast, simple ensemble methods that leverage rich textual context accompanying time-series can outperform strong baselines on TimesX.

cs.LG↗

arXiv2026

Rethinking Post-Training Recipes for Multimodal Time-Series Forecasting

Time-Series Foundation Models (TSFMs) excel at zero-shot unimodal forecasting using numerical data, but unlike LLMs they cannot consume multimodal, non-numerical context that often shape real-world trajectories. In this work, we bridge this gap and argue for a multimodal time-series forecasting approach that post-trains LLMs to act as context-guided revisors over strong numerical TSFM priors. We introduce PostTime, a post-training recipe combining Supervised Fine-Tuning (SFT) and Reinforcement Learning with Verifiable Rewards (RLVR), along with a methodology to generate automated reasoning traces for forecast revisions. PostTime teaches an LLM to generate context-conditioned forecast interventions -- decisions to revise, preserve, or ignore the TSFM prior based on the multimodal context. We evaluate this approach on the TimesX multimodal forecasting benchmark using a Gemma-3-4B LLM and TimesFM-2.5 TSFM, and show that it significantly outperforms standalone TSFMs, LLM-only baselines, and existing multimodal forecasting approaches.

cs.LG↗

arXiv2024

Multi-Modal Forecaster: Jointly Predicting Time Series and Textual Data

Current forecasting approaches are largely unimodal and ignore the rich textual data that often accompany the time series due to lack of well-curated multimodal benchmark dataset. In this work, we develop TimeText Corpus (TTC), a carefully curated, time-aligned text and time dataset for multimodal forecasting. Our dataset is composed of sequences of numbers and text aligned to timestamps, and includes data from two different domains: climate science and healthcare. Our data is a significant contribution to the rare selection of available multimodal datasets. We also propose the Hybrid Multi-Modal Forecaster (Hybrid-MMF), a multimodal LLM that jointly forecasts both text and time series data using shared embeddings. However, contrary to our expectations, our Hybrid-MMF model does not outperform existing baselines in our experiments. This negative result highlights the challenges inherent in multimodal forecasting. Our code and data are available at https://github.com/Rose-STL-Lab/Multimodal_ Forecasting.

cs.AI↗

arXiv2024

In-Context Fine-Tuning for Time-Series Foundation Models

Motivated by the recent success of time-series foundation models for zero-shot forecasting, we present a methodology for $\textit{in-context fine-tuning}$ of a time-series foundation model. In particular, we design a pretrained foundation model that can be prompted (at inference time) with multiple time-series examples, in order to forecast a target time-series into the future. Our foundation model is specifically trained to utilize examples from multiple related time-series in its context window (in addition to the history of the target time-series) to help it adapt to the specific distribution of the target domain at inference time. We show that such a foundation model that uses in-context examples at inference time can obtain much better performance on popular forecasting benchmarks compared to supervised deep learning methods, statistical models, as well as other time-series foundation models. Interestingly, our in-context fine-tuning approach even rivals the performance of a foundation model that is explicitly fine-tuned on the target domain.

cs.LG↗

arXiv2023

A Combinatorial Approach to Robust PCA

We study the problem of recovering Gaussian data under adversarial corruptions when the noises are low-rank and the corruptions are on the coordinate level. Concretely, we assume that the Gaussian noises lie in an unknown $k$-dimensional subspace $U \subseteq \mathbb{R}^d$, and $s$ randomly chosen coordinates of each data point fall into the control of an adversary. This setting models the scenario of learning from high-dimensional yet structured data that are transmitted through a highly-noisy channel, so that the data points are unlikely to be entirely clean. Our main result is an efficient algorithm that, when $ks^2 = O(d)$, recovers every single data point up to a nearly-optimal $\ell_1$ error of $\tilde O(ks/d)$ in expectation. At the core of our proof is a new analysis of the well-known Basis Pursuit (BP) method for recovering a sparse signal, which is known to succeed under additional assumptions (e.g., incoherence or the restricted isometry property) on the underlying subspace $U$. In contrast, we present a novel approach via studying a natural combinatorial problem and show that, over the randomness in the support of the sparse signal, a high-probability error bound is possible even if the subspace $U$ is arbitrary.

cs.DS↗

arXiv2023

Transformers can optimally learn regression mixture models

Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models that present the intriguing possibility of providing general-purpose prediction methods, even in this mixture setting. In this work, we investigate the hypothesis that transformers can learn an optimal predictor for mixtures of regressions. We construct a generative process for a mixture of linear regressions for which the decision-theoretic optimal procedure is given by data-driven exponential weights on a finite set of parameters. We observe that transformers achieve low mean-squared error on data generated via this process. By probing the transformer's output at inference time, we also show that transformers typically make predictions that are close to the optimal predictor. Our experiments also demonstrate that transformers can learn mixtures of regressions in a sample-efficient fashion and are somewhat robust to distribution shifts. We complement our experimental observations by proving constructively that the decision-theoretic optimal procedure is indeed implementable by a transformer.

cs.LG↗

arXiv2023

A decoder-only foundation model for time-series forecasting

Motivated by recent advances in large language models for Natural Language Processing (NLP), we design a time-series foundation model for forecasting whose out-of-the-box zero-shot performance on a variety of public datasets comes close to the accuracy of state-of-the-art supervised forecasting models for each individual dataset. Our model is based on pretraining a patched-decoder style attention model on a large time-series corpus, and can work well across different forecasting history lengths, prediction lengths and temporal granularities.

cs.CL↗

arXiv2023

Linear Regression using Heterogeneous Data Batches

In many learning applications, data are collected from multiple sources, each providing a \emph{batch} of samples that by itself is insufficient to learn its input-output relationship. A common approach assumes that the sources fall in one of several unknown subgroups, each with an unknown input distribution and input-output relationship. We consider one of this setup's most fundamental and important manifestations where the output is a noisy linear combination of the inputs, and there are $k$ subgroups, each with its own regression vector. Prior work~\cite{kong2020meta} showed that with abundant small-batches, the regression vectors can be learned with only few, $\tilde\Omega( k^{3/2})$, batches of medium-size with $\tilde\Omega(\sqrt k)$ samples each. However, the paper requires that the input distribution for all $k$ subgroups be isotropic Gaussian, and states that removing this assumption is an ``interesting and challenging problem". We propose a novel gradient-based algorithm that improves on the existing results in several ways. It extends the applicability of the algorithm by: (1) allowing the subgroups' underlying input distributions to be different, unknown, and heavy-tailed; (2) recovering all subgroups followed by a significant proportion of batches even for infinite $k$; (3) removing the separation requirement between the regression vectors; (4) reducing the number of batches and allowing smaller batch sizes.

cs.LG↗

arXiv2023

Long-term Forecasting with TiDE: Time-series Dense Encoder

Recent work has shown that simple linear models can outperform several Transformer based approaches in long term time-series forecasting. Motivated by this, we propose a Multi-layer Perceptron (MLP) based encoder-decoder model, Time-series Dense Encoder (TiDE), for long-term time-series forecasting that enjoys the simplicity and speed of linear models while also being able to handle covariates and non-linear dependencies. Theoretically, we prove that the simplest linear analogue of our model can achieve near optimal error rate for linear dynamical systems (LDS) under some assumptions. Empirically, we show that our method can match or outperform prior approaches on popular long-term time-series forecasting benchmarks while being 5-10x faster than the best Transformer based model.

stat.ML↗

arXiv2022

Efficient List-Decodable Regression using Batches

We begin the study of list-decodable linear regression using batches. In this setting only an $α\in (0,1]$ fraction of the batches are genuine. Each genuine batch contains $\ge n$ i.i.d. samples from a common unknown distribution and the remaining batches may contain arbitrary or even adversarial samples. We derive a polynomial time algorithm that for any $n\ge \tilde Ω(1/α)$ returns a list of size $\mathcal O(1/α^2)$ such that one of the items in the list is close to the true regression parameter. The algorithm requires only $\tilde{\mathcal{O}}(d/α^2)$ genuine batches and works under fairly general assumptions on the distribution. The results demonstrate the utility of batch structure, which allows for the first polynomial time algorithm for list-decodable regression, which may be impossible for the non-batch setting, as suggested by a recent SQ lower bound \cite{diakonikolas2021statistical} for the non-batch setting.

cs.LG↗

arXiv2022

Trimmed Maximum Likelihood Estimation for Robust Learning in Generalized Linear Models

We study the problem of learning generalized linear models under adversarial corruptions. We analyze a classical heuristic called the iterative trimmed maximum likelihood estimator which is known to be effective against label corruptions in practice. Under label corruptions, we prove that this simple estimator achieves minimax near-optimal risk on a wide range of generalized linear models, including Gaussian regression, Poisson regression and Binomial regression. Finally, we extend the estimator to the more challenging setting of label and covariate corruptions and demonstrate its robustness and optimality in that setting as well.

cs.LG↗

arXiv2022

On Learning Mixture of Linear Regressions in the Non-Realizable Setting

While mixture of linear regressions (MLR) is a well-studied topic, prior works usually do not analyze such models for prediction error. In fact, {\em prediction} and {\em loss} are not well-defined in the context of mixtures. In this paper, first we show that MLR can be used for prediction where instead of predicting a label, the model predicts a list of values (also known as {\em list-decoding}). The list size is equal to the number of components in the mixture, and the loss function is defined to be minimum among the losses resulted by all the component models. We show that with this definition, a solution of the empirical risk minimization (ERM) achieves small probability of prediction error. This begs for an algorithm to minimize the empirical risk for MLR, which is known to be computationally hard. Prior algorithmic works in MLR focus on the {\em realizable} setting, i.e., recovery of parameters when data is probabilistically generated by a mixed linear (noisy) model. In this paper we show that a version of the popular alternating minimization (AM) algorithm finds the best fit lines in a dataset even when a realizable model is not assumed, under some regularity conditions on the dataset and the initial points, and thereby provides a solution for the ERM. We further provide an algorithm that runs in polynomial time in the number of datapoints, and recovers a good approximation of the best fit lines. The two algorithms are experimentally compared.

stat.ML↗

arXiv2022

Dirichlet Proportions Model for Hierarchically Coherent Probabilistic Forecasting

Probabilistic, hierarchically coherent forecasting is a key problem in many practical forecasting applications -- the goal is to obtain coherent probabilistic predictions for a large number of time series arranged in a pre-specified tree hierarchy. In this paper, we present an end-to-end deep probabilistic model for hierarchical forecasting that is motivated by a classical top-down strategy. It jointly learns the distribution of the root time series, and the (dirichlet) proportions according to which each parent time-series is split among its children at any point in time. The resulting forecasts are naturally coherent, and provide probabilistic predictions over all time series in the hierarchy. We experiment on several public datasets and demonstrate significant improvements of up to 26% on most datasets compared to state-of-the-art baselines. Finally, we also provide theoretical justification for the superiority of our top-down approach compared to the more traditional bottom-up modeling.

cs.LG↗

arXiv2021

Cluster-and-Conquer: A Framework For Time-Series Forecasting

We propose a three-stage framework for forecasting high-dimensional time-series data. Our method first estimates parameters for each univariate time series. Next, we use these parameters to cluster the time series. These clusters can be viewed as multivariate time series, for which we then compute parameters. The forecasted values of a single time series can depend on the history of other time series in the same cluster, accounting for intra-cluster similarity while minimizing potential noise in predictions by ignoring inter-cluster effects. Our framework -- which we refer to as "cluster-and-conquer" -- is highly general, allowing for any time-series forecasting and clustering method to be used in each step. It is computationally efficient and embarrassingly parallel. We motivate our framework with a theoretical analysis in an idealized mixed linear regression setting, where we provide guarantees on the quality of the estimates. We accompany these guarantees with experimental results that demonstrate the advantages of our framework: when instantiated with simple linear autoregressive models, we are able to achieve state-of-the-art results on several benchmark datasets, sometimes outperforming deep-learning-based approaches.

cs.LG↗

arXiv2021

Hierarchically Regularized Deep Forecasting

Hierarchical forecasting is a key problem in many practical multivariate forecasting applications - the goal is to simultaneously predict a large number of correlated time series that are arranged in a pre-specified aggregation hierarchy. The main challenge is to exploit the hierarchical correlations to simultaneously obtain good prediction accuracy for time series at different levels of the hierarchy. In this paper, we propose a new approach for hierarchical forecasting which consists of two components. First, decomposing the time series along a global set of basis time series and modeling hierarchical constraints using the coefficients of the basis decomposition. And second, using a linear autoregressive model with coefficients that vary with time. Unlike past methods, our approach is scalable (inference for a specific time series only needs access to its own history) while also modeling the hierarchical structure via (approximate) coherence constraints among the time series forecasts. We experiment on several public datasets and demonstrate significantly improved overall performance on forecasts at different levels of the hierarchy, compared to existing state-of-the-art hierarchical models.

cs.LG↗

arXiv2021

On the benefits of maximum likelihood estimation for Regression and Forecasting

We advocate for a practical Maximum Likelihood Estimation (MLE) approach towards designing loss functions for regression and forecasting, as an alternative to the typical approach of direct empirical risk minimization on a specific target metric. The MLE approach is better suited to capture inductive biases such as prior domain knowledge in datasets, and can output post-hoc estimators at inference time that can optimize different types of target metrics. We present theoretical results to demonstrate that our approach is competitive with any estimator for the target metric under some general conditions. In two example practical settings, Poisson and Pareto regression, we show that our competitive results can be used to prove that the MLE approach has better excess risk bounds than directly minimizing the target metric. We also demonstrate empirically that our method instantiated with a well-designed general purpose mixture likelihood family can obtain superior performance for a variety of tasks across time-series forecasting and regression datasets with different data distributions.

stat.ML↗

arXiv2021

Session-Aware Query Auto-completion using Extreme Multi-label Ranking

Query auto-completion (QAC) is a fundamental feature in search engines where the task is to suggest plausible completions of a prefix typed in the search bar. Previous queries in the user session can provide useful context for the user's intent and can be leveraged to suggest auto-completions that are more relevant while adhering to the user's prefix. Such session-aware QACs can be generated by recent sequence-to-sequence deep learning models; however, these generative approaches often do not meet the stringent latency requirements of responding to each user keystroke. Moreover, these generative approaches pose the risk of showing nonsensical queries. In this paper, we provide a solution to this problem: we take the novel approach of modeling session-aware QAC as an eXtreme Multi-Label Ranking (XMR) problem where the input is the previous query in the session and the user's current prefix, while the output space is the set of tens of millions of queries entered by users in the recent past. We adapt a popular XMR algorithm for this purpose by proposing several modifications to the key steps in the algorithm. The proposed modifications yield a 3.9x improvement in terms of Mean Reciprocal Rank (MRR) over the baseline XMR approach on a public search logs dataset. We are able to maintain an inference latency of less than 10 ms while still using session context. When compared against baseline models of acceptable latency, we observed a 33% improvement in MRR for short prefixes of up to 3 characters. Moreover, our model yielded a statistically significant improvement of 2.81% over a production QAC system in terms of suggestion acceptance rate, when deployed on the search bar of an online shopping store as part of an A/B test.

cs.IR↗

arXiv2021

Bandits with Stochastic Experts: Constant Regret, Empirical Experts and Episodes

We study a variant of the contextual bandit problem where an agent can intervene through a set of stochastic expert policies. Given a fixed context, each expert samples actions from a fixed conditional distribution. The agent seeks to remain competitive with the 'best' among the given set of experts. We propose the Divergence-based Upper Confidence Bound (D-UCB) algorithm that uses importance sampling to share information across experts and provide horizon-independent constant regret bounds that only scale linearly in the number of experts. We also provide the Empirical D-UCB (ED-UCB) algorithm that can function with only approximate knowledge of expert distributions. Further, we investigate the episodic setting where the agent interacts with an environment that changes over episodes. Each episode can have different context and reward distributions resulting in the best expert changing across episodes. We show that by bootstrapping from $\mathcal{O}\left(N\log\left(NT^2\sqrt{E}\right)\right)$ samples, ED-UCB guarantees a regret that scales as $\mathcal{O}\left(E(N+1) + \frac{N\sqrt{E}}{T^2}\right)$ for $N$ experts over $E$ episodes, each of length $T$. We finally empirically validate our findings through simulations.

cs.LG↗