arXiv subjects

Millen Kanabar

Publications and source records attributed to Millen Kanabar.

3 recordsLinked to original sources

arXiv2026

Minimax bounds for watermarked and masked recursive discrete distribution estimation

Watermarking has been proposed as a way to identify synthetic samples in estimation settings where no metadata is available to distinguish them from real samples, but its precise effects remain unexplored. In the absence of a distinguishing mechanism, it has been shown that adding synthetic samples significantly reduces the marginal efficacy of new real samples. In this work, we study the minimax loss of such recursive discrete distribution estimation in the presence of watermarks in contrast to the unassisted and oracle-assisted losses. When the fraction of real samples vanishes asymptotically, we provide a lower bound that shows that it is impossible to improve performance by adding watermarks unless the false negative rate of detection also vanishes. Additionally, we show that in most regimes, the worst-case losses of a sequence of simple deterministic estimators match the corresponding lower bounds up to constants. Finally, we propose masking, a randomization procedure that narrows the gap in the remaining regimes to a Jensen gap. We conjecture that a tighter lower bound argument can close this gap.

cs.IT↗

arXiv2026

Model non-collapse: Minimax bounds for recursive discrete distribution estimation

Learning discrete distributions from i.i.d. samples is a well-understood problem. However, advances in generative machine learning prompt an interesting new, non-i.i.d. setting: after receiving a certain number of samples, an estimated distribution is fixed, and samples from this estimate are drawn and introduced into the sample corpus, undifferentiated from real samples. Subsequent generations of estimators now face contaminated environments, a scenario referred to in the machine learning literature as self-consumption. Empirically, it has been observed that models in fully synthetic self-consuming loops collapse -- their performance deteriorates with each batch of training -- but accumulating data has been shown to prevent complete degeneration. This, in turn, begs the question: What happens when fresh real samples \textit{are} added at every stage? In this paper, we study the minimax loss of self-consuming discrete distribution estimation in such loops. We show that even when model collapse is consciously averted, the ratios between the minimax losses with and without source information can grow unbounded as the batch size increases. In the data accumulation setting, where all batches of samples are available for estimation, we provide minimax lower bounds and upper bounds that are order-optimal under mild conditions for the expected $\ell_2^2$ and $\ell_1$ losses at every stage. We provide conditions for regimes where there is a strict gap in the convergence rates compared to the corresponding oracle-assisted minimax loss where real and synthetic samples are differentiated, and provide examples where this gap is easily observed. We also provide a lower bound on the minimax loss in the data replacement setting, where only the latest batch of samples is available, and use it to find a lower bound for the worst-case loss for bounded estimate trajectories.

cs.IT↗

arXiv2022

Mismatched Rate-Distortion Theory: Ensembles, Bounds, and General Alphabets

In this paper, we consider the mismatched rate-distortion problem, in which the encoding is done using a codebook, and the encoder chooses the minimum-distortion codeword according to a mismatched distortion function that differs from the true one. For the case of discrete memoryless sources, we establish achievable rate-distortion bounds using multi-user coding techniques, namely, superposition coding and expurgated parallel coding. We study examples where these attain the matched rate-distortion trade-off but a standard ensemble with independent codewords fails to do so. On the other hand, in contrast with the channel coding counterpart, we show that there are cases where structured random codebooks can perform worse than their unstructured counterparts. In addition, in view of the difficulties in adapting the existing and above-mentioned results to general alphabets, we consider a simpler i.i.d. random coding ensemble, and establish its achievable rate-distortion bounds for general alphabets.

cs.IT↗