In order to fully unlock the transformative power of distributed ledgers and blockchains, it is crucial to develop innovative consensus algorithms that can overcome the obstacles of security, scalability, and interoperability, which currently hinder their widespread adoption. This paper introduces HybridChain that combines the advantages of sharded blockchain and DAG distributed ledger, and a consensus algorithm that leverages decentralized learning. Our approach involves validators exchanging perceptions as votes to assess potential conflicts between transactions and the witness set, representing input transactions in the UTXO model. These perceptions collectively contribute to an intermediate belief regarding the validity of transactions. By integrating their beliefs with those of other validators, localized decisions are made to determine validity. Ultimately, a final consensus is achieved through a majority vote, ensuring precise and efficient validation of transactions. Our proposed approach is compared to the existing DAG-based scheme IOTA and the sharded blockchain Omniledger through extensive simulations. The results show that IOTA has high throughput and low latency but sacrifices accuracy and is vulnerable to orphanage attacks especially with low transaction rates. Omniledger achieves stable accuracy by increasing shards but has increased latency. In contrast, the proposed HybridChain exhibits fast, accurate, and secure transaction processing, and excellent scalability.